First let me say hello, and welcome to the board.
I've never been convinced that mixing T&M and competitive bid is a great idea. I'll try to explain:
In T&M work, the owner bears more risk but (sometimes) saves some money, i.e. - if the job goes well. On the other hand, in bid work, the contractor bears the risk of how the job goes. So it's a matter of who bears risk, and who reaps the reward for that risk.
In the case where a contractor offers a bid price as an NTE (not to exceed) and then works T&M up to the NTE point, the owner reaps some monitary benifet if the job goes well, and the contractor receives less than his bid amount.
If the job does not go well, the contractor still has the risk, and all of a sudden it's a firm fixed price deal.
Bidding work is the same as taking risk, and if the job goes well, the profit is the contractors reward. Why would he agree upfront to give some of it away?
Offering a price estimate (different than a firm fixed price bid) and then doing straight T&M work is OK, but the NTE part only serves to shift potential risk to the contractor, and shift potential rewards to the owner.
Just my thoughts,
Radar
