DaveM

The Nagoya 771 is a dual band amateur band antenna...which judging by its length, looks like a 1/4 wave on 2 meters and 5/8 wave on 70 cm ham band.  I personally would not use this antenna for GMRS.  This antenna would need to see some sort of ground plane to radiate properly, in addition to properly loading for lowest reflected power.  As i am a Motorola person, I am not certain about the construction of the Btech radio in regards to the case acting as a proper ground plane.  If it does not have a metal chassis, or metal impregnated case, and is only relying on the SMA connector for a ground plane, I am not so certain that your goal of antenna trimming will ever be achieved reliably.

Heliax is the only way to go, especially if in the future, you need to run duplex communication.  When I set mine up, I opted for 7/8" Andrew Heliax, with N- Connectors of course.  I also dived in and acquired a DB420 antenna set up in an omnidirectional pattern.  RG 400 makes perfect patch cabling...double shielded, yet flexible.  My wife had a small coronary when she first saw it up, but she got over it in less than 24 hours.  Antenna, feedline, and grounding are where all the money and effort should be directed.  Do it once and do it right.