1) Upgrade my Electrum 2.6.4 to 3.0.2 and just open the old wallet file in 3.0.2. I assume I don't have to use the seed here and the old 2 factor solution using google auth will still work without additional setup? Reason for the upgrade is to avoid issues with an older version.
I would recommend that you ONLY upgrade as far as v2.9.3... just to make the next step easier, as I'm not 100% sure that ElectronCash v2.9.4 will play nicely with a v3 wallet.
3) Use the seed from my 0 BTC electrum wallet to import into a BCH wallet like Electron Cash installed on another computer. Do I need to disable the 2 factor login on my electrum wallet before doing this?
You should restore your 2FA in ELECTRUM... disabling 2FA functionality during the restore... then you should be able to open that wallet using ElectronCash... as it is disabled, it will have two of the 3 private keys and you'll be able to create/sign the appropriate BCH transactions.
When you say I should be able to open the wallet using ElectronCash do you mean that I (at this point) can just open the Electrum wallet file in ElectronCash and my BCH will then be available in the wallet? Or do I need to import the seed or private keys?
5) Claim my BTG by exporting the private keys from the electrum wallet and importing them into the android wallet coinomi app. Potentially transfer them to my BTG address on the Nano S if possible. Do I need to disable the 2 factor login on my electrum wallet before doing this?
This won't work... as Abdussamad has pointed out, you can't just export your private keys from an Electrum 2FA wallet and import them into Coinomi to get BTG... instead you need to follow a process like this:
https://bitcointalk.org/index.php?topic=2550529.0Yes... it really IS that long and complicated... PLUS you need to have BitcoinGold Core downloaded and synced for it to work.
Wow that is a complicated guide. Is there any chance that there will be an easier way in the future? Because then I would just wait with claiming the BTG as I'm not sure I would get all the steps correct here anyway.