You're welcome. I know you're probably going for a more self-sufficient way of activating heating up on your Streetfighter by multiclassing with a Black Jacket and using a blunderbuss, but may I suggest an alternative, party-dependent setup for a Streetfighter? It still relies upon using a blunderbuss, but instead of equipping a blunderbuss directly on your Streetfighter and using the Powder Burns modal, you equip Serafen's Hand Mortar on another party member and take its Blinding Smoke upgrade. Blinding Smoke adds a Disorienting effect to its auto-attacks which fires out in a cone and affects allies and enemies alike. By merely positioning your Streetfighter in between your Hand Mortar-user and enemies, you can reliably keep Heating Up activated on your Streetfighter. The Blinding Smoke attack also targets Will and works on grazes which is very beneficial for a Streetfighter that would want to keep their other defenses like Deflection high in order to counteract the Flanked status that comes with Disoriented. Another nice facet about the Blinding Smoke effect is that it is an attack that does no damage so it won't take away charges of spells like Mirrored Image.
You would still wanted to deal with the fact that Disoriented is a nastier T2 Perception Affliction that adds on a 50% recovery penalty which is counter-synergistic to the Streetfighter's recovery bonus. Luckily, a very easy way to deal with this is to upgrade Eder's starting Saints War Armor which gives Perception Resistance and will downgrade Disoriented to a more manageable Distracted perception affliction. These two pieces of gear are available fairly early, though it may take you some time to gather the necessary materials to upgrade them. You'd also be stuck with using Hand Mortar on another party member to enable your Streetfighter's bonus, but I find that a party member with high-ish Intellect can reliably keep the duration of Blinding Smoke active on the Streetfighter while alternating between attacks with another, dual-wielded weapon, like Fire in the Hole to pair with it, or firing off the occasional spell -- a dual mortar setup is pretty nice setup for a lot of builds so you don't exactly have to twist my arm for me to want use it, personally. Granted, another downside is the opportunity cost of not being able to take the alternative Point Blank shot enchantment on Hand Mortar for the extra damage. Yet another issue that you'd have to overcome is protecting your other frontliners besides the Streetfighter who are standing in front of the Hand Mortar-user so that they don't suffer Blinding Smoke's effects. Fortunately, the Captain's Banquet food bonus can give you Perception Immunity, but be prepared to shuck quite a lot of oysters depending on the number of front-line party members you have.
I know this may all seem like a chore, but it's honestly my favorite, relatively painless way of getting a Streetfighter to work, especially when I want the Streetfighter to be able to use weapons other than a blunderbuss with Powder Burns. This party setup would also free you up to multiclass your Streetfighter with something else besides a Black Jacket, since you seem a little disappointed by needing to dedicate several slots for blunderbusses to do the Powder Burns swap and the lack of being able to use your Fighter side's Disciplined Barrage. Instead, you can multiclass your Streetfighter with another class that has higher, non-Perception Inspiration accuracy buffs and defenses to counteract the Flanked and Distracted status. Cipher is a nice option, for example, for the Borrowed Instinct's big boost of accuracy and defenses. Paladin is another good option for the accuracy or armor aura, the accuracy bonus while using Flames of Devotion, and the Clear Head passive ability which gives you Perception Resistance, allowing you to then use a different armor than the Saint's War Armor.
It also sounds like you're leaning more towards the Black Jacket side in your original Streetfighter / Black Jacket post. I have some suggestions on Black Jackets too if you'd like.