Does it make more sense (timewise) to claim all the forks directly on coinomi? Except for BCD (IIRC), you can claim the rest directly with them; you move the private keys less times, make a single sweep, and can even dump everything for BTC at the same place.
Yes, that's faster. But I prefer to sign transactions offline, and BCH is the most valuable Forkcoin. Coinomi still doesn't let you split BCH-A though, and indeed BCD isn't supported.
What do you think about Bither wallet?
Sorry, I don't understand why I would need to get the private keys from my old wallet. Could you please elaborate?
Before you can claim the forked coin will need to sweep your old wallet using your private keys or seeds. Thats why you asked to move your BTC to new wallet.
EDIT: Is it to import them into those electrum wallets so I don't need to download the other coin's blockchain?
Yes, Electrum wallet is lite than Bitcoin core but you need to download the wallet from the official site electrum.org and verify the wallet.