I graft a few mulberries every year; usually collect dormant scionwood in late Feb/early March, wrap in moist paper toweling in a ziploc bag in a fridge(no fruit -ethylene gas is detrimental to the buds) until spring, when the seedling rootstock commences growth - then I do a simple bark graft(see link below), but I've done simple whip, whip & tongue, cleft grafts and all work OK; I just prefer the bark graft.

If things have already broken dormancy, you may be better off waiting until late June and doing some T-budding from the super-sweet tree onto your seedling rootstocks. After the buds have callused in(probably within 2-3 weeks), you could 'force' the buds by pruning the roostock off just above your bud placement - or leave them 'parked' until next spring, and prune off anything above the bud just before they break dormancy. Just search for 'T-budding' - should be plenty of info out there on the 'net.

Here is a link that might be useful: Joe Real's Bark-Grafting Tutorial

or you find a grafter who will do it for a nominal cost ...

call gee tree farm or girards nursery ...

as noted.. its the wrong time of year ... but nothing like planning ahead ... you might need to provide some small understock in the fall.. so they can pot them and be ready for winter grafting .... [and if your mulls are like mine.. you have them EVERYWHERE .. lol]

grafting itself .. is simple .. the problem is the aftercare with humidity tents.. irrigation.. temps.. etc ...

if you like the challenge. .. give it a go ... if you are into immediate gratification ... hire it out

good luck

ken