I don't think that the COE can release information on "Sealed Bids" under FOIA beyond the current successful bid unless the awarded contract is challenged. In addition I don't think that the FOIA is relevant to unsuccessful bids due to a specific exclusion.
In other words you can't find out what I bid on a contract if I didn't win it. All COE contracts include reams of regulations by reference. You would have to do some heavy duty research of those inclusions.This can really make your head hurt and probably best done by an attorney familiar with contract law. Remember you are in fact contracting with the Department of Defense which has the funds for the COE in it's budget.
As a former Park Attendant contractor from 1999 to 2014 I think I would have been very upset if one could simply demand to know what my bids on previous and current contracts were under the FOIA in order to use that proprietary information to under bid me.
After all that's the point of "Sealed Bids."
On Edit:
Just to add. You in fact may not have had the lowest bid for the contract you win.
For example, if I bid several contracts in the same district and I am the low bidder on several of those contracts the COE will select which is the most advantageous to the government to award me.
That is to say if I bid $10.00 a day lower on one location and only $5.00 per day lower on the one you bid more then me you could win it. The government will award me the one I was $10.00 low on.
It is not something where you can bid several different positions in a District, be low bidder on several and pick the one you want. The COE will offer you one without reference to the others. If you decline that offer you have in effect declined all bids made for that District.