Hi Michael, in general I think you've got a good approach at BRRR here with some live-in sweat equity. This is similar to what I have done so far (bought a two-fam, rented out one unit while fixing mine, fixed 2nd unit on tenant turnover, then moved out and now rent both for improved cash flow).
It's difficult to give specific advice on your HELOC approach with what you've given us so far for a few reasons. The primary reason is I'm having a hard time following your math, the numbers given don't really line up - I'll get to that in a moment. And second I think you need to really characterize your risk/return for both approaches you've outlined and see how that fits your personal appetite for risk. Third, I think you need to do more research on achievable rents for these units. That's not to say you haven't, but right now it's not clear how you're getting your estimates for what market rent is and if your units would in fact draw those rents given your location, competition, tenant base, etc.
So about the numbers: you're saying the 4-plex gets 2100/mo now but the listed rents are 490 + 550 + 525 + 575 = 2140. If you're living in one unit then your rent roll is really just whatever the other 3 units will provide, are you planning to stay in that one unit, or move to a private residence/next investment once the rehab is complete? Also it sounds like you have two tenants leaving so your total rent right now could be as low as $525/mo until those others are filled.
Mortgage is given as $1200/mo but is that PITI? Is there PMI as well? With only one tenant in place your monthly expense is at least $700 currently, if you add in a HELOC payment what does that look like near term?
If we assume each unit needs $4k in repairs/upgrades then you're looking for a HELOC of at least $12k - will that come from this property's equity or from your 2-door investment property? I ask this because the source will determine your ability to write off the interest payments on your taxes - it may be a business expense or personal expense, or possibly not deductible at all. This is a question for your CPA/tax adviser that I can't answer but it is one you need to ask to get the full picture and may sway your choice of equity source.
Finally, on the expected rents, how are you determining that $650 is a realistic number? Do you have local comps getting that much? Have you gotten the opinion of a local realtor who places tenants? I have done this, it was exceptionally useful! A local agent placing renters will have the best knowledge of current prices and tenant expectations - they may be able to give you advice on desired upgrades you may not have considered which will get you better return for your renovation dollars.
The other thing that makes me question the $650 target is you say you have 2 tenants who already balked at rent going to $600 and opted to leave instead. That tells me they have other cheap options in the area, so make sure whatever improvements you are making will actually get you your desired tenant/rent. It might be prudent to try to fill at least one vacancy at $600 now to determine how likely higher rents will fare. Again, a rental agent will be helpful in knowing current prices, paying a half or full fee to get them to screen and place a tenant would have the additional benefit of having this conversation with them to gauge your market.
Ultimately since you have some flexibility of schedule and funds I would say do your first live-in upgrade from existing funds and get the other units rented closer to full market rate. Save that rental income and then when your first unit reno is complete you will have an exact picture of the time and cost to do each of the next units. At that point you will find out what rent the updated unit will really fetch and that should inform your decision on how best to fund/repair the next 3.