How would you suggest I time things?
Your partners' employer needs to do the full and proper RLMT process first to prove to HO that there are no settled/British or EU citizens suitable for the job. The job adverts (on two sites) cannot be made so difficult so as to favour only your partner and exclude everyone else. You don't state what job (title) your partner does??
I can resign now and serve 3 months notice, meaning both our visas would be void in 3 months.
I would strongly suggest you do NOT resign until you know for sure your spouse has a Tier 2 General visa. Curtailment DOES NOT happen so fast.
Can he start the process for a Tier 2 general visa now, while still on his dependent visa? (Ie go to his home country next month to start the process, then return to the UK on the dependent visa)?
Once the CoS is issued AFTER the whole RLMT process (must be done for 28 days), then your partner can return to home country and MUST apply from there. Your partner will not be able to return to the UK during this process. Once your partner is successful in getting a Tier 2 General, they return to the UK and you can then apply for a Tier 2 dependent visa.