Ignorance of sellers and realtors/buyer brokers part. Bidding wars are realtor/bank games to maximize sales price. No lender is going loan anymore than what house appraises for. So, if you bid high and get the house, but it appraises for less, you will have to pony-up the difference. However, with the VA loan you have the option to walk away. I don't believe you could do that with a conventional.
If you really want the house, offer to pay all the closing or ask for 3-5% seller-paid closing. An offer like this, with a low bid, can make a difference to a seller who has several high bids with all seller-paid closing costs. Of course there are other offers to sweeten the deal, but YMMV. Despite the housing debacle, it is not a buyers market, although the talking heads would like you to think it is.
If you're working with a broker/realtor, who is on the hook for their commission? Considering they could get up to 5% of sales prices, your GFE seems low.
I recently closed with a VA loan, and I live in market where bidding wars and home over-valuation are common practice. Is is what it is. 
I wanted to add that foreclosures and short sales, while maybe a great deal, can add to an already aggravating process. Particulary the time element and they're sold as-is, which could mean additional exspense to repair home structure or replace appliances. I lost many bids on these types of properties. I finally wound up with home from a regular sale. I happened to be in the right place at the right time. I made an offer and asked for $5000 in seller-paid closing costs. Another VA loan buyer offered substantially more and asked for all closing cost paid by seller. The seller took my offer.