I'm imagining two best uses for these cards.

1)Beefing up investigators who already have 3 in a stat, such as Diana's strength, Luke's evasion, Jim's intellect, etc. so they can pass basic tests that don't let them use spells to swap stats - most notably those on treacheries or scenario cards.

2)Giving the option to commit out-of-class skills to Mystic staples for power plays. Deduction onto Rite of Seeking, Vicious Blow onto Shriveling, etc.

A fun upside: you can combine this with the Chuck Fergus to play it fast & free at the end of your turn. if you’re going to run Chuck, this card goes from “sometimes it’s useful with quick thinking or against aloof enemies“ to "an enemy dies and you draw a card."

This one is for Survivor Tony as a precursor to Brute Force.

Anyone else would prefer to play an actual weapon, but Tony's always been plagued by a lack of good weapons early to the point where he'd consider Kukri. The .41 Derringer's great but the Mauser C96 has a tendency to jam. This is when Tony needs to Improvise. Tony's rich enough that he won't mind paying 1 resource just for a +1 for the followup +1 +1 damage.

I am wondering if Prescient is a good add to Sister Mary, especially paired with Olive McBride, it makes it really likely that you pull a token, so it turns Prescient almost into Resourceful.

Aim at Ward of Radiance and you got yourself a good encounter prot against non- treachery cards.

Disclaimer: I haven't run any detailed math here and haven't searched all the cards for some uber combos. I just made my thoughts regarding this card, the reviews and my personal game experience so far.

If I were able to give this card a revamp I would change two things to make it (in my view) a compatible big gun beside the others.
I would increase the cost to 6 and change the text to something like this:

Uses (8 ammo.)
Spend 1 ammo: Fight. you get +1 for this attack. This attack deals +1 damage. As an additional cost you may spend up to three additional ammo. You get +1 and deal +1 damage for each additional ammo.

with this, the overall performance would be much closer to the other guns and you have essentially two fire modi:

1. single fire: for 4 XP you get 8x 2 damage at +1 for 6 ress. This is a 25% discount over the .45 Automatic (my "gold standard" for weapons). This discount comes with all the drawbacks of a big gun: requires two hands at once, one big target for asset hating treacheries.
2. burst fire: here comes the flexibility (and the justification for XP)! Gain action compression by spending the exact amount of bullets you need for your enemy. Lose a portion of your discount.

Let's see how this compares to the other big guns in our arsenal

1. Shotgun: spending 4 ammo gives you 2 shots at +4 for 5 dmage. Same burst potential, more reliable damage, less synergy with extra ammo cards. I think the "new BAR" has the advantage here.
2. Lightning Gun: spending 2 ammo gives 4 shots at +3 for 3 damage. So one action more than the lighting gun, at a lesser to hit chance. Again harder to reload. I think both weapons are roughly on par, depending on the campaign and player needs.
3. Flamethrower: spending 3 ammo gives 2 shots at +4 for 4 damage and leaving you with to ammo left. Between this two it comes down to flexibility vs. burst. Both weapons are capable of doing max 16 damage, but single shot "new BAR" needs double the amount of actions. Again I think both cover different terrain and would see both their use in game.

Right now, I am no big fan of a big gun guardian. But with the flexibility of the "new" BAR? Yes, could see me using it as a mid campaign upgrade!

PS: I could think of a third "automatic fire" mode with a second action option which could look something like this:
Exhaust M1918 BAR and spend 5 ammo: Fight. You get +2 for this attack. If this attack is successful, instead of its standard damage, you may assign up to 4 damage among enemies engaged with you (any additional damage adds to this total). Enemies damaged by this attack will not attack during the enemy phase.
So you have some suppression mechanic at the cost of damage. I don't know how such a mechanic would balance but flavor wise I think this would be a cool addition.