As Jay alluded to and others have noted here and there, your time will be better spent tuning up and getting good with what you have in hand, rather than going out and throwing money at new solutions. Why? Because those new tools all have limitations and learning curves, just like the tools you already have and with which you have actual firsthand experience. This is a fine handicraft and as such, there are no shortcuts, no silver bullet, no easy street. It's time to take the time to master your tools and don't get suckered in by the tool manufacturers' slick marketing (they want your $$); this is why we all participate in the craft, it's about the learning and the gradual mastery, and the freedom that comes from that.
The jigsaw idea: By design, these will at best provide you a very rough cut that needs lots of truing up with...a plane!! LOL. The only ones I will consider are the Festool (hold on to your wallet) and the Bosch, which are the ones Festool copied via a ~4-year long collaboration with Bosch. So you will be throwing in another ~$300 minimum to get a quality tool that is not designed to accomplish what you hope to accomplish and still need that plane to become ready for assembly.
Very importantly, jigsaw blades are unsupported, so even though one can cut a nice straight pencil line, that's only at the top surface, and below that pencil line, the blade will bend and flex and wander as it follows the growth rings in the work piece. The end result will be a work piece that needs so much reworking that the wise woodworker will need to layout a daunting waste allowance that is much bigger than the finished size and there's always the possibility that that won't even be good enough and you might have to redesign your finished piece to accommodate the dimensions of the individual components -- that's a path to failure.