“Simulationist” is a good word for it. Games of that era, like early 40k, all seemed to do that, presumably because they were more closely related to RPGs. Cinematic rather than tactical. I’m okay with that, particularly because you can switch to Alpha Strike for a different type of game.
But I don’t think Classic is tactically too light a game. The modifiers put the focus on movement and positioning, as it should be. You try to get an edge in modifiers and the game is long enough for a small difference to gradually win the battle.
I think the big issue is the number of turns. 40k isn’t actually all that quick, it just has a high enough casualty rate that a 6-turn limit is usually more than enough. Fewer turns hurt a game, imo, because they de-emphasize movement (e.g. less payoff for spending time getting into a good position), but they speed it up. Point is, a quick fix could be to use more highly-skilled Mechwarriors by default. Less quick: a general increase of mechs’ firepower/armor ratios.
As a new player, I’d also say that reducing some table look-up rolls to a single die would help. Does it really make sense to blow up just one-third or a torso? Could hit location rolls be a d6, or maybe a larger die that had words on it? You’d have to rebalanced headshots, sure.
And I’d consider making LRMs and cluster ammo hit every location evenly. Defender fills in one dot in each location (he chooses the order) before spilling over into a second dot in each location. Too big a change to make without a thorough rebalancing - just something to think about.