Alex - it is a bit more simple than you would think. You obtain a construction to perm loan and they pay off the first lien. I am financing a new construction in bham; feel free to shoot me a note and I can tell you the lenders in Michigan that offer competitive construction financing. I think the forum rules prohibit posting that information.
As a side note, Fannie underwriting guidelines note for a construction loan the following: land owned for >1 year, the FMV of the land + construction costs= your value (V) in LTV; land <1 year they use the acquisition price. Effectively, the 25k you have in equity in the lot contributes towards a virtual down payment to meet LTV requirements. Two lenders I know of go to 90 and 95 LTV in Michigan.
200k (land FMV) + 250k construction costs= 425k
total land (cost basis) + improvements= 400k
95 LTV of 425k is 403k. You would only need 3k cash required to close (based on your estimated costs)