In all my years of riding Amtrak sleepers, I've never witnessed anyone having their carry on luggage 'refused' by the car attendant. In recent years, I've seen everything from people boarding with the biggest rolling suitcases I've ever seen and leave them in the baggage area downstairs. And on that trip, someone else had what looked like a full size collapsible baby crib. Needless to say, the baggage area was overloaded that trip and most of the time, there were a couple of bags in the vestibule area that had to be moved to the other side at the next stop, etc. Part of a normal trip for the attendant, in my opinion.
Depending on how much 'stuff' you're taking out for your son, considering that you'll have your own luggage, some of which you'll need to access during the trip and will need to fit your roomette. I typically travel with an airline carry on size rolling suitcase that fits under the seat and a 'gym bag' of whatever I'll need multiple times per day. Depending on whether your roomette is in a Superliner I or Superliner II, you'll either have a narrow closet - maybe 5" wide, or a U-shaped hook to hang clothing on. That's what I usually pack in my suitcase. I'd estimate that in the roomette, 2 under-the-seat suitcases and a gym bag that I put on the 'steps' and perhaps a smaller crumple-able bag that would fit in the closet/hanger area floor. Everything else has to be stored downstairs.
Simply put, whatever the two of you can schlep down the platform to your sleeper (front of the train for the SEA section) would be the 'practical' limit in my opinion. I've seen collapsible hand trucks used by some passengers. The ones at Harbor Freight might be sufficient - just don't put more than the maximum weight specified in the instructions indicates. Being a former Milwaukee area resident, I think the only stations in Wisconsin that is still staffed is Milwaukee and La Crosse. Columbus shows checked baggage as well in the timetable, but I vaguely recall reading that the Columbus agent position had been abolished. If you're boarding at Columbus, definitely verify there's an agent to check your bags. As for checking bags at unstaffed stations goes, I have no clue with the conductor will handle checked baggage or not. Presumably, they are supposed to do that at unstaffed stations.
In all, including checked bags and carryons, I'd probably limit yourself to 4 items per person - otherwise, you'll quickly regret bringing anything more with you. Otherwise they're falling over / out of your arms / off the pile / whatever. Strapping them together might help, but in the end, it may slow things down. Your physical condition is also a factor which may limit how much you can lug. And at Seattle, you'll have to schlep everything once again. Hopefully, your son will meet you on the platform at the station. And if he drives a car the size of a VW Beetle, that may be a major problem of where to stow the luggage.
Lastly, should you decide to box up some things and ship them, Amtrak -may- still handle items like that. If so, and it's available at your boarding station, check the prices for a 70 pound box vs 70 pound checked item. Alternatively, UPS, Fedex, and the Post Office are a good alternative. Using them, first and foremost, pack <whatever> so that an adult can stand on top of the box and it won't be crushed. Anything breakable such as china or stereo equipment needs to be very well padded. A couple of giant-size bubble wrap things and a 15 pound item will likely be broken if the box gets dropped enroute. Items like glassware and most everything else in the kitchen would be better sold/donated and your son buy new in Seattle. The cost of shipping would likely exceed the cost of new items. Considering that the shipping companies pile boxes floor to ceiling in a trailer, if your package is on the bottom and cannot withstand a momentary 'crush force' of 100 pounds of other packages on top of yours and the truck hits a bump, the downward crush force may double or triple. Also put a packing slip in each box indicating what's in it, along with yours and sons address and phone numbers. I worked for almost 3 years at a Fedex Ground hub and and when boxes break open or the tape gives way, trying to match up loose items to any of a dozen or more other packages that broke open goes far more easily if they know what's supposed to be inside. If it can't be determined, the loose 'stuff' goes to Salt Lake City and will be auctioned in lots if not claimed by the rightful owner. One more thing...be generous with your shipping tape. Don't waste your money on Scotch brand 'shipping tape'. I use rolls of Duck brand of shipping tape I get at Walmart. Be sure to completely circle the box with a continuous strip of tape to hold the flaps down. We had one large volume corporate shipper that put only one strip of tape along each closing seam with 1.5" around the corner and on the side. We'd get 20-30 boxes per night that the tape unsealed itself at both 1/5" ends and the stuff came out. Fortunately, one of my acquaintances worked in the quality control department. It took about 6 months of repeatedly telling her 'more tape' before the shipping department got the message. Going all the way around the box guarantees that the flaps won't pop open from too little tape. If it's a box of pots and pans, the compact weight of them would suggest 2 or 3 times around the box with tape to keep everything inside.
Also, when it comes to shipping, as long as it's under 70 pounds per box and 'regular' dimensions (not a package with a broom inside or a fiberboard poster), any of the carriers will be happy to ship it. Oddball shape items cost a bunch more to ship. The UPS Store will even pack it for you and supply the box(es) for a fee. As shipping prices are dictated by weight, distance, and speed, shipping the heavier items and carrying (or checking) lighter things will cost more money. Also, I'm aware from my own experience that UPS has an 'expected revenue per cubic inch' algorithm in their pricing. Shipping a bed pillow in a box will cost about the same as if the box with the same dimensions had 20 pounds in it. They likely calculated that on average, every full trailer would bring in X dollars of revenue and make sure it gets at least that much. I discovered this by shipping stuff I've sold on ebay.
Lastly, there's no such thing as 'fragile'. Every package gets treated and handled just like all the others. I think the Post Office charges more if a package is marked 'fragile'. But the limits of what they'll cover if it gets broken probably doesn't change if it's fragile or not. Maybe 30 years ago already, I was at the Post Office dropping off a package a couple weeks before Christmas. The lady in front of me had a box that was 12-15" on each edge clearly marked on all sides 'fragile'. After she paid, got her receipt and turned to walk out, the P O clerk took the box and did a rebound off the rear wall about 10' behind him and the package dropped into the big rolling canvas bin.