A mixer really seems like the right solution. It's exactly what you want to do... Mix or select different inputs (to your effects chain). How do you expect to mix without a mixer?
And, a simple little mixer costs less than most effects pedals. I wonder if one of the guitar effects companies makes a "guitar mixer"?
However, you have a couple of unusual requirements... You need both instrument-level & line-level inputs, and you need an instrument-level output. (Most mixers have line-level outputs.)
If you know how to "build electronic stuff", you can make a line-level-to-instrument-level reducer with 2 resistors (a
voltage divider circuit).
Or, you can build a
summing amplifier with an op-amp (and a power supply or a couple of batteries, and a few other parts). Mixers are designed around summing amplifers, so you are building a non-adjustabel mixer. You can alter the resistor values to mix line & instrument levels together, or you can add a couple of pots and, you've built a mixer.
Hmmmm.... With enough experimentation,
you could probably build a fixed-passive mixer with just two resistors. Take the voltage divider circuit, and instead of connecting one resistor to ground, connect that one to your line-in, and the other resistor goes to the guitar. You need high impedance (high resistance) to avoid "loading" the guitar, and the line-input needs a higher value for more voltage/signal drop. So, get a handful of high-value (high-ohms) resistors and experiment. I'd start with 10M ohms for the line-in resistor, and 1M for the guitar. (Or maybe 100M and 10M.)