No plum,.. I would cut them down really good now, branches like a foot or so down to the main trunk this year. Let them grow new wood [water sprouts] and graft next spring onto these about 10 inches out. Any good pie and sweet cherries, you could get a instant 10 variety going next year.

I would suggest same as konrad -- cut branches way way back to about a foot from the trunk, allow new sprouts to come out of the "stumps" this season, then next spring try grafting some good tasting varieties to the sprouts. The tree will look goofy for a few years, but after 6 or 7 years it will look almost normal again and you'll have a great crop of great tasting cherries of whatever varieties you like. There are a lot of good online resources about how to do this. Look up stephenhayesuk on YouTube as I know he's got more than one video about "grafting over" an old tree (in his case it's with apples but the concept for cherries is the same).

Agreed.

Your trees are well established, use them for grafting hosts. Has to be other types of cherry, but you could go hog wild and graft as many types of cherry branch to them as you can get your hands on. Have a veritable cherry fruit salad tree.

Pie cherry trees are good for whip and tongue grafting as well as budding in the summer. If you don't like Montmorency, you could graft on sweet cherry. I have read warnings about this, but I dont know if I believe them. IT is a different species.
John S
PDX OR

It is possible to graft sweet cherry onto tart cherry, but it most often does not do the best. It is also possible to graft plum onto cherry, but I think the compatibility level between the two may be poor (I'm not entirely sure though).

The plum rootstock Adara (Prunus cerasifera) is compatible with cherry. Ken Coates, who has been a commercial grafter for almost 30 years, used Adara as an interstem to graft cherry onto plum.

http://www.goodfruit.com/goodbye-plum-hello-cherry/

I received an email last week from Stark Bros saying that Luther Burbank was a long time collaborator with them (famous for plums etc) and he grafted over 200 varieties of cherry onto one tree that was successfully fruiting.

So I say go crazy with it, play mad scientist cause you're sure to get something of an improvement on it. I'd just make sure to prune it well so when the good fruit does come in you can net the tree from the birds. No sense in doing all the hard work and then serving up a buffet for them only.