You can create vlans no problem, however each vlan will need its own subnet range, so no, there isn't a way to create vlan without changing ip address or subnet mask/default GW of all hosts.
Migrating to a 10 network could be good or unnecessary depending on your environment, follow ip addressing assignment best practices by researching it.
Well you could calve up your existing /22 in to smaller networks i guess? but you will have to change the mask and default gateway of all your hosts including the FW.
Slowness, hmm, depending on what these hosts are doing, they could be generating a lot of broadcast traffic, which isn't really needed. There could be a whole bunch of things for slowness. Check the link utilisations of links, CPU, memory etc... to see where the bottleneck is.
If you re-IP your network, its extremely likely you will have to edit your security policies, especially if you move on to a 10 network scheme.
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