Another option would be original MiteeBite clamps, and they can be used for other work holding aswell.
They're not cheap, but they are a very versatile low profile clamping system!
50642 is the kit you'd most likely need, or you could buy a pack of just the cam clamps 50206 (come in a pack of 10) and make the other bits yourself. But having just checked the catalogue, I've just realised you can get packs of 2 t-slot clamps, which for 8mm slot is 50422.
WDS is the only online UK stockist I'm aware off, and you'll need to add '590-' in front of the mitee bite part no.s.
If you're interested and willing to wait, I'm on the process of designing a jig that'll use some of the 50206 clamps, but I won't be needing the full pack, so would be willing to sell you a couple.
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Sticking with what you've got, you could grind/machine down the top side of the end of the clamp fingers so they fit in the vice groove. The grinding/machining doesn't have to be pretty, as long as the underside is still flat.
As a temp fix, get some longer bolts and use the clamp set to clamp on the top of the vice, be that either on top of the jaw(s) and/or on the top of the main body provided there is enough room behind the moving jaw.