@protostache...
I'm in the same boat, so let me give you my thoughts...
First, from what I can tell, the "cash reserve" can still be in some retirement accounts (like a RothIRA or 401k). You'd have to check with a mortgage broker, but don't take anything OUT of the accounts yet.
Second, you want AT LEAST 6 months (a year is better) after a hard pull when buying a house - so don't do any loans or anything unless they won't run your credit.
Third, make sure you can carry both mortgages with your monthly income or you won't be approved - the first mortgage counts for "debt" when calculating what you can afford. (I know you mentioned this, just be sure with the new increase in HELOC you are still ok.)
And yes, you must have it at least 3 months in the account - at least for the places I'm looking at.
So timeline:
6 months out - take any credit/loans you need to let your score rebalance
4 months out - take out cash and sit on it
3 months out - get your old place ready
2 months - 1 month - start house buying process (it usually takes 30-60 days to close) - also list your place in this timeline.
good luck, hope it goes well for you (and me!)