I need to record a VGA signal, and so need a way to get it into HDMI, HD-SDI, or DVI.

Product that could do it are TV One C2-2355A, 1T-C2-760, Gefen EXT-VGA-2-DVISP, and there are many others.

Do you know of any place/person in L.A. (Culver City area) who rents scan converters? I found VER but they're booked and $350/day is way over budget.

Not real familiar with a scan converter, but have you tried online rental stores?
LensRentals.com - Rent Video > Accessories > Recorders (http://www.lensrentals.com/rent/video/accessories/recorders)

I bought a similar product to this recently and it works very well despite the low cost. Not entirely sure the very expensive options are worth it except for the fact they offer greater versatility and functionality:

PC VGA Audio Video to HDMI HDTV Converter Adapter S1132 | eBay (http://www.ebay.co.uk/itm/PC-VGA-Audio-Video-HDMI-HDTV-Converter-Adapter-S1132-/250858981952?pt=UK_Computing_CablesConnectors_RL&hash=item3a685c4a40#ht_3711wt_907)

Geoff