Aloha @Sam T.! I did a similar strategy to what you're trying to accomplish last year. It's difficult to obtain a single LOC in that amount you're looking for, but the way I did it was, I shotgunned my application out to several local banks all at the same time. This way the banks didn't flag it like they would have if I had applied month after month. I basically was approved for a total of $120k by the time they finally started denying me ($50k, $25k, $25k, $20k).
Here's the catch - you really have to read the fine print in the loan documents. Many of the unsecured PLOCs that I have all ask for interest only (at around 10%) PLUS 2% of the outstanding principal balance. The outstanding balance is the important key here, sometimes they wont tell you in the online account information is in the paperwork. Let's do a quick example calculation if I maxed out my PLOCs = $120,000 borrowed at an average 10% interest rate:
$120,000 * 10%/12 = $1,000 interest due PLUS $120,000 * 2% outstanding principal balance = $2,400. Total due to banks is $3,400. This is where you could easily go underwater real quick while you're waiting on your refinance to go through. Just be careful. I have a lot of credit to draw from, but I strategically pull from it when I really need to, and never the entire amount.
Also agree with @Jason D.'s statement on the DTI ratio when you refinance. When I did my first cashout refi, I told my bank the money would immediately go to paying off the LOC which was true. I didn't have any issue, but my balance was only $40k to repay back to my LOC.
I found it best if you could borrow some of the funds from friends or family and use the LOC to cover the balance. The benefit here is that you could ask friends/family for interest only payments (not interest plus 2% of principal)
Good luck!