So yeah, Electron Cash works just fine. Mostly.
This is a problem I have with Electrum as well, but back when I was mining, I have one address that had 600+ transactions. I managed to consolidate them down in Electrum and send them to my new Electrum wallet.
But when I try to send off my BCC using Electron Cash, the whole wallet hangs up when I import that address's private key... It's a nightmare. So I essentially have a whole BTC in that address that is stuck for the time being.
I've tried about 10 times to get it working with no results. I'm even thinking of downloading the entire blockchain with bitcoin unlimited to send it that way, but it's gonna' take a while. o_o
I assume you didn't do this consolidation until after the fork? If so, you may truly be stuck until a fix is released. If you consolidated before the fork, you should be able to use the seed from your new Electrum wallet in an instance of Electron Cash. That should work because the consolidation should've resulted in just a single UTXO.
Just out of curiousity, what happens when it hangs? Is it still using CPU time per a task manager? If it is still grinding away on the CPU, maybe let it sit for a long while and see what happens.
Electrum used to have a "coin control" functionality, but it looks like it has lost that capability at some point. That would've allowed you to send each individual UTXO from among the 600+, but I don't know whether that would've of worked in any case.
Edit: You have the right idea in that your final option would be to download and sync a full node wallet, and then import that private key. I assume you meant you'd download the Bitcoin Cash version of Bitcoin Unlimited.
Hmm, I just figured out that on current Electrum wallets, coin control is hidden by hiding the "Addresses" tab. To view it, hit CTRL+A. The problem is, this functionality seems to be missing from Electron Cash.
EDIT: Perhaps CTRL+A doesn't work on my Electron Cash because it has only a single non-zero UTXO right now. If I learn differently, I'll update.