Hey! I'm using a similar-ish setup with a 1x30 and unfortunately the best solution I've found is an angle grinder. I'm generally hesitant to recommend it to others, but your jigsaw setup sounds terrifying. The longer it takes, the more chances for a mistake, and an angle grinder will cut that inch in seconds.
The main injury comes from bonded abrasive cutoff discs that degrade and literally shrink as you use them- they resist force in only one direction, any fractures, lateral force or pinching of the disc can make it shatter into the sharp projectiles. But they sell metal discs that are much safer, with abrasives layered on top of a metal backing. The diamond abrasive will rub off over time, but the disc itself won't degrade structurally.
There's still a chance of cutting yourself if the entire tool kicks back against you, so you should absolutely watch some safety videos- different sections of the wheel will walk the tool in different directions, and you need to be focused the entire time. But you're using the tool for its intended purpose, and I think using an underpowered alternative built for something else is going to be more dangerous over time.
You can also use a high tension hacksaw specifically meant for cutting metal, which isn't THAT slow and dirt safe. The teeth are tiny and cut mostly by friction.
On a budget, I think it's going to be easier to think of wood/metal cutting as separate functions. A portable bandsaw would work for both, but it starts around $150 and you need to fabricate/buy a special table to use it in that orientation safely plus switch blades. Circular saws require specialty blades to cut metal and require a really stable working surface, while being heavier. Carbon steel is really tough, not every metal cutting tool or blade is going to work well for it. There are a lot of inexpensive solutions to cutting/shaping wood- saws, rasps, chisels, dremel bits, spokeshaves, or just buying wood in closer sizes- but relatively few ways to cut high carbon steel.
An impact driver will be worse than a drill for high carbon steel.
Honestly, I've found hand filing with a really good file to be much faster for thinning the knife than a 1x30. I use the belt grinder for the first bevel just to get close to the center line, then clamp it down to a board and draw file to raise the bevel up the belly of the knife. It's like you're lopping the top off a pyramid, focusing that peak- with a decent file, the metal almost comes off in curls. Just make sure it's double cut (teeth running in both directions), and brush it occasionally to unclog the teeth. After most of the material's gone, I switch back to the belt grinder, but it really speeds things up and you get a clear view of the knife as you're working.
If you decide not to get an angle grinder, this is how I would spend the budget. The pullsaw naturally cuts straight, but if you're off at the start it's hard to correct compared to the traditional saw. The kutzall rotary burr is REALLY efficient at removing wood, if it fits your rotary tool
Pull Saw ($14) OR Olson Wood Saw ($12)
Nicholson Bastard Double Cut File ($8)
If you get the angle grinder, make sure to get the metal backed discs and protective equipment (safety goggles or face shield and a respirator) and don't use it indoors.
Good luck!