Give them a deadline of 7 - 14 days to respond - in writing.

I would do that on your next move unless you find a really great deal.  4 months to move into, potentially rehab to add value, find renters, pack up and PCS out seems like a tight timeline.  

The numbers you mention here sound pretty tight and you may experience negative cashflow in the beginning.

It is (and should be) tightly regulated.  

Offer them $ amount (my general rule of thumb - 20% more than monthly payment) and a deadline (exact date of 30 days from today i.e.) and what will happen if not (I will have to pursue legal actions.)3.

If you focus on the number of doors, and you are getting close to your deadline, you will make a bad deal.

After holding costs, closing costs, appraisals, rehab draws and other misc fees, that is extremely tight!

Inventory is a little tight right now across most property types so we're jumping on properties within minutes of going on market! 

To remove the timeframe of a 5 month deadline, I began thinking outside the box which is why I am seeking guidance on getting a vacant land loan.

Even if there is no filing requirement, you may want to consider filing to obtain your suspended loss carryforward.If the LLC is multi-member, the general deadline will be March 15.If the LLC is single member, the general deadline is April 15.