Most lenders release as improvements are made. That's how lenders protect their collateral. I would place greater emphasis on finding lenders who offer the best construction loan administration experience (those who process and release draws quickly, those who will release for materials on site as opposed to installed, those who don't hold back retainage). I would much rather have that for the life of the project than a lender who may release some money up front (which is unlikely) but otherwise provides a difficult construction loan administration experience.
For some of my larger projects I will transfer some of the project management/overhead fee to a "mobilization fee" which is paid out on the initial draw and my lenders have always accepted this. However I only include this in my larger new construction builds, not smaller rehabs. It may be a way to advance some of the loan proceeds earlier in the project. You can also gross up some of your earlier trade line items such as demo, framing etc. and decrease back end items like kitchens, appliances to access some funds earlier. I used to do this with my earlier smaller rehabs but it's more difficult to do this with larger projects because my lenders typically want to receive copies of all major subcontract agreements.