Autofire isn't a problem; quite frankly not all weapons were created equal and it is especially tailored to wiping out groups of people. Some weapons are natually much higher in power to give the players or apposing NPC's pause for thought; if autofire didn't exist, then there wouldn't be any real value in taking a heavy weapon with it compared to a rocket launcher. The heavy blaster rifle is meant to be that instrument that is designed to either suppress or mow down large groups of minons, in the same way that a person with high presence, cunning or corc can have a strong influence during the talkative encounters.
That being said, the GM needs to present more situations where it might not be possible to have that weapon available for an encounter. For example within a civilised setting or a smuggling port the offical there (even if they aren't "official" ) will usually set up rules on what is/isn't acceptable at the port and to leave any weapons that don't meet those regulations aboard the ship. E.g. only pistols, weapons of a certain size category must be kept in a case. No droids. e.g. to provide situations where the party might not necessarily have access to all their tools or to raise the risk factor by having to smuggle those tools in, within briefcases, trollies/whatever. Though if you get caught the consequences should be quite hefty. Fines, detainment and other interesting complications.
My GM had a lot of problems initially because he never applied any of those restraints, therefore the heavy gunner basically took his heavy blaster rifle wherever he went, until it came to a head in a session where the gunner was posing as a dignitary in a high class, high security casino, and when things went wild he simply stated. "I will draw my heavy blaster rifle and open fire." which caused a huge argument because quite frankly "no one would have been allowed within the function room of this planets upper crust with a weapon that could potentially clear out this planet's government in 2 minutes.". Since then, naturally introducing certain expectations and enforcing security checks for illegal items per person, it had become possible to tailor the encounters, having tons of minon groups for the full out war encounters while being able to scale back for those lesser encounters, unless the party was particularly inventive.
It's not your fault for taking what you specialise in as frequently as possible,
but rather then using the rules to play passive/aggressive moderator and the other attempting to wiggle out of them, you two should be hashing out the terms of engagement or what is and isn't reasonable within a particular environment, until then your game will be doomed to eventually collapse.
Once that starts to happen and he starts using squad rules to represent groups of minions, the problem should naturally clear itself up. This means also being able to compromise within those environments. Your character shines during the full blown military ops, just you might want to consider a different load out when within certain environments with restrictions.
In short, drop the house rules, enforce narrative restrictions and be flexible.