However, I was surprised to discover that a Gauss Rifle is a good weapon against BA (one shot, one down)
Expensive weapon against BA. The Gauss rifle is feared by 'Mechs because it can decapitate one regardless of their weight class, so using it against BA is a bit of waste. That said, the Inner Sphere has very few things that can kill Elementals with one shot, so it is a bit of "damned if you do, damned if you don't" situation, if a point of Elementals is a large threat.
Against Inner Sphere medium BA, anything that does 10 damage is nearly always sufficient.
I'll note that basically anything the Inner Sphere has will have difficulties against the Clans circa '52. In straight fight, the Clans have advantage. But use your tanks from ambushes (hidden units), along with other dirty tricks, it gets easier. Though the tanks probably aren't making it back home all the same, not after the angry Clanner whose paintjob you ruined comes after them.
Anyway, your tanks. With their mediocre mobility, single weapon systems and weak armor, they're more like fire-support vehicles. Not a bad idea for vehicles, and a given the limits you've given to yourself, you've done good job with them. Their use requires some care though, both of them will attract more attention than they can handle otherwise.
Budget-wise, there's certainly something appealing using several smaller vehicles with massive combined firepower. Though logistically, it is unlikely you can effectively spend all your budget on lighter units, you'd need to provide all the crews and maintenance and whatever.
But in BV-balanced game, that won't work out so well, as it is you can get a couple of your Gauss vehicles (and some extra) for a single Challenger mk. X, but the Challenger will most likely win that fight (at least i'd bet on the Challenger).
One reason BattleTech vehicles are loaded with weapons is that they can actually fire them all at once, unlike most 'Mechs which are heat-limited (though naturally double heat sinks mitigate this to an extent).
Existing canon vehicles (especially the big, expensive ones) don't necessarily have good combination of weapons, possessing something for multiple ranges usually, but they may have alpha strike capability way higher than many 'Mechs, and thus make for large threats.
Also don't discount the threat of infantry against vehicles, especially in cities where infantry shines. There's a reason many vehicles mount anti-infantry weapons, and relying on escorts may not always work out. That said, in a tightly designed vehicle, spending tonnage on a MG and half a ton of ammo probably isn't particularly useful.