Wood – stack headers in a load bearing wall

There is no problem flush framing the LVL in the ceiling as you suggest, provided it physically fits in the space available. If the LVL is placed directly over the 4x10, the ceiling joists will need to be cut to make room for the LVL. If this cutting keeps them from bearing on the 4x10, they need to be shored up until the LVL and hangers can be fitted. A temporary ledger on the 4x10 will suffice. Since LVLs can be narrower than sawn timbers, shoring/ledger may not be needed.

You might consider removing the 4x10 beam to open up the new opening so it is taller. Once you remove the supporting walls, it will more or less fall down anyway, unless it is well attached to the new LVL, essentially hanging it beneath the LVL. Why leave it there? It's not doing anything but getting in the way. Unless it's hiding the end of a soffited area, the taller opening would be an added benefit of flush framing the new LVL.

Based on your description of the loading, I wouldn't be too concerned about supporting it at all unless you're going to leave the framing out for any significant period of time (days for example). If anything it might sag a fraction of an inch, but you'll true it up when the new header goes in. You'll want to remove the old one first and re-frame that section of the wall, then cut in your new rough opening and put the new one in. Pretty simple, and I've done this numerous times with patio doors.

If you're concerned about the weight, consider that there are quite a few houses out there dating from the time before building codes became common that don't have proper headers over windows and doors at all. I've done several jobs where I had to install headers that were missing in the first place. Also, I've done a couple garage demolitions where I had a hard time removing enough structure to make it collapse.