I am guessing the beam is just holding the rafters ties up also.
If you want to remove the beam, do this.
Otherwise you should be able to tie in the beam to the face of the new header
I think you are going to need taller header than 2x6, or 2x8. Guessing more like 2x12
Tie the beam to the face of the 2x12
Remove the support between the two small doors holding up the beam.
Is there another reason you want to raise the beam?
You had a garage door installer out and he did not bring up issues with putting in a new 16 foot wide door. So there must be enough head room above the door. (As he didn't mention the need for a low headroom door, also assuming that person is a competent installer).
Sounds like you need to...
It sounds like you have roof trusses. You should get an engineer or a truss designer to help you modify your existing trusses.
Is this getting city permits and inspected, if so they will require engineered drawing of modifying your trusses.
Consider this. If your roof collapsed in the...
Wow
That's really nice.
I have been wanting a wood cabinet like that, just haven't come across on in good shape at a price that I want to spend.
seem like they used to pop up more often in the past
Try contacting the manufacturers tech support. Call them when you are in the garage. They may be able to help you do some tests to trouble shoot your problem.
The garage door opener companies (Chamberlain and Genie) that I've dealt with in the past had great tech support.
My wild guess is a...