It all depends on what the CPUs are inside the HS21s but from what it sounds like you've already tried, I bet you're going to have to give up. We're in the same boat. Our HS21's are completely incompatible with our HS22's because of the processor families. Our HS21 has E5450 CPUs. The newer CPUs in the HS22's can't be dumbed down to an E5450 even with VMotion Compatibility Mode turned on (they can only "dumb down" so much if that makes sense).
In our case though, we've found it most cost-effective to simply sunset our HS21s because of these factors:
1) They have paltry memory compared to our current standard (32-48GB vs. the 256GB blades we buy now)
2) Upgrading memory on that model of blade is prohibitively high (we could buy a new blade with newer memory for the same price as only upgrading memory in the HS21s - don't know why but the memory used in the HS21 must be hard to come by)
3) If you divide the cost of your fully populated/configured chassis by 14, you'll have the "cost per slot". Turns out for us that the cost-per-slot we pay is more expensive than the HS21s themselves. That essentially means that it's more expensive for us to have the HS21s that to not have them and allow their slot to be taken up by a more dense, newer blade. Since we're upside down on our HS21 blades, we're phasing them out. In other words, we'll keep using them but if all chassis slots are full, we'll throw away an HS21 before we'll buy a new chassis.
4) Besides when you consider that one HX5 can replace what? 8 HS21s... phasing them out isn't a difficult choice. The vSphere CPU licenses you'll recoup for deployment on future blades alone is pretty significant. Upgrade one HS21 blade's vSphere licenses up to Enterprise Plus (if it's not there already), then replace up to 8 HS21s with a single HX5 (using that upgraded vSphere Enterprise Plus license for the HX5). Then you have 12CPU sockets of vSphere licenses at your disposal. Using methods like this, we rarely need to ever purchase additional vSphere licenses. We just keep recycling them on more and more dense CPUs.