doing this: https://duckduckgo.com/?q=apricot+custom+grafting&t=ffcm&ia=web

i came up with this: https://www.turkeycreektrees.com/services

i have no experience or knowledge of them ... ken

A lot depends on why the existing tree is unhealthy, if for instance it has a condition such as a virus buildup that may simply continue in the replacement plants after the grafting. Or maybe even prevent the scions from taking well. If it is a known named variety that has been maintained as a single clone you can effectively continue the same plant by instead buying a (hopefully clean) specimen from a commercial source.

Very important point Embothrium. I was going to bring that up too, but it sounds like this tree is old and venerable enough to be either of unknown origin or a seedling. Ofdm can correct me if I'm wrong...

Actually it is quite unhealthy. There are mushrooms growing on the trunk in some places and the top half of the trunk is hollow. A couple of branches are propped up by 4x4s.

I wish I knew what the variety was. Based on descriptions I find online it could be Blenheim but I'm not sure. Dark yellow when ripe with reddish tinge. 1.75-2" in length. Freestone. Ripens 2nd week of June. Very productive. 4 medium sized moving boxes worth of fruit.

The trunk diameter is about 2 ft above the root flare so it must be an older variety.

Apricot trees have a short life span if yours is old it might be the end of the line. Grafting is easier than you t but honestly you probably like the fruit so much because you are comparing it to store bought apricots . If you buy a Blenheim tree you will be just as happy with the fruit imo. You cou even get a multi graft apricot and spread your harvest out

I found several rootstocks for apricots. Cummins Nursery has a Mariana GF8-1 full size rootstock for Apricots, They 're $2.75 each. The shipping is $20 estimated when I added one to my cart. I bought apple rootstocks from them last year without problem. I checked Fedco, no apricots. I checked Willimette they have 3 varieties but only sell a 100 minimum. I didn't check at Grandpa's cause they wanted $45 shipping minimum last spring. You should order early, first of the year, once they run out they're out. They all seem to ship once and that's it. Fedco allows you to choose early or late, that's it.

That sounds expensive, but if you buy a seedling it may cost you double that. Another thought I had was that since you're trying to save your tree and you've never done this before you should consider buying more than 1 rootstock. Even if you put two grafted trees in the same hole you've got a guarantee for only $2.75 more.

I did 7 apple grafts last spring and all are doing fine. They all sent a shoot up from the tip of the scion and no other shoots, so I'm thinking you need to be careful of the top most bud. Growth varied from 4 inches to 30 inches. All the growth is whips, no branching. I also planted a couple of the rootstocks without grafting for backup trees. The M.111 (semi-full) grew about 4 foot, next to it an M.7 (semi-dwarf) grew about a foot.

Google "whip and tongue" graft. You'll find video's and articles. I used a retractible safety knife and teflon plumbers tape which I had. I bought grafting tape on eBay for a few bucks which included shipping. I used the teflon tape instead of parrafin which you'll find in your supermarket if you ask for "gulfwax". I'd suggest you cut the bottom off a plastic half gallon milk jug make a hole in the center and use it for a finger guard.

Good luck.