TM... just for clarification purposes, SSDI is not SSI. Obviously all comes from the same taxes but no one specifically pays into SSI. Your annual stmt from SSA shows how much you've paid into SSA over the years. You'll see it's never even enough to cover your Medicare costs down the road much less your SS retirement checks. How much you pay is never going to cover the amount you collect.
I agree with TM. The point of it is long term planning, not short term. You're right, he'll probably get nothing in terms of cash. But why not put the money you are spending now on medical bills in a special needs trust for him? So get him on Medicaid (which could mean switching some docs, pharmacies, etc). As Fran has to eloquently posted here you could have some problems with SSA re the application and on an ongoing basis because you're paying for so many things for him. So what I'd do is set up an account in his name specifically for his SSI check. Let him manage that account which will have a minimal balance but will be his spending money. Put whatever you can spare that would have gone to medical expenses into the trust every month. Then when he needs something that Medicaid won't pay for you buy it out of that money. Long term then there's money in a trust for him. 30 or 40 years down the road if he needs a van, needs to make wheelchair modifications to a home, buy some new high tech chair, bath lift, computerized automatic door openers, etc there's money there. You really can't anticipate what kind of technology there might be for him that Medicaid won't pay for when we're gone.
No matter where you live the SSA system is the same. You may decide to move to a place with a bed open that you want to grab but can't because the application process will take months. It's not a matter of whether or not he's qualified, it's paperwork in their office.
Reminder: special needs trusts vary by state so be sure to tell the attorney that you intend to move.
Maybe this is obvious but in my mind the ideal situation would be to have whatever you leave him go to the trust. The trust buys a house for him and his choice of roommate to live in, hires staff, etc. So down the road he's not a tenant subject to the rules of some agency but his own landlord. If he's got the capability (with the help of a trustee of the trust) to make decisions why not give him aome control over his life later. This can all be managed through a lawyer familiar with spec needs law...the trust, the non-profit to own the house, etc.
As to medical insurance, assuming the premiums aren't costing you a lot of money, keep it on him if you really can't switch docs or there's something it pays for that Medicaid won't. The Medicaid will then be secondary.
Bottom line, let your money benefit him down the road and let Medicaid pick up the excess bills now. Set up the SSI now so when he really needs to be approved for it you won't have to go through the process.