Instead of sending it to two different busses, just duplicate the track. Put a high pass filter on one copy, and a low pass filter on the other copy and make sure the cutoff frequencies are the same.
Then just put whatever plugins you want on one track or the other.
This was done quite often in the analog world, where one tape track was multed to two or more channels on the mixing console. Then the same track could have two different mixes that could be switched between (using mutes) or layered on top of each other. The way to do the same thing in the DAW is with track duplication. Note that duplicating a track does not create a separate copy of the media files used by the track, so you're not taking up more hard drive space with this trick.
The reason why making the cutoff frequencies the same ensures no total attenuation or boost at the crossover point is because by definition, the cutoff frequencies are the 3 dB down points. At the exact crossover frequencies, each of the high and low tracks are 3 dB down. When they are combined, they add up to the original power level, because 3 dB down is half the power. The other aspects of the filters you want to match for smoothest crossover is the slopes. Once you pick 6 or 12 or 18 or 24 or whatever dB per octave, make both the highpass and lowpass filters have that slope.
All that said, once you put different plugins on the different high and low tracks, you're going to make them different from each other to the point that having a smooth crossover region is pretty much meaningless. If you tape saturate the lows and not the highs, then you've just changed the the levels and loudness of one while leaving the other the same, which means your crossover region is now a mixture of something different with something the same. There's no preventing that - that's part of what you are deliberately doing to the audio.
Another way to approach the whole thing is to leave the original track as is and then just low pass the duplicate track. Saturate the crap out of the "low" track - way more saturated than you want it to sound - and then turn it all the way down. Now slowly bring it up while playing back until you are adding in the amount of the low saturation that you want. If the whole thing seems like it has too much low end at this point, you can add a low shelf to the original track to drop it down slightly.
No matter what, your whole goal as a mixer is to make it sound good, not to make it sound... anything else. Don't worry about weird things happening in the crossover region. Worry about it sounding bad. If it sounds bad, isolate why and then change it. Maybe it turns out to be the EQ settings, you just have to change them to make them sound better, but there's no one set of EQ settings that someone else can tell you will sound good. You have to figure it out based on the actual musical material you are working with. It's like asking what paint colors to use to paint a flower in a picture. There's no one answer. Your answer is the answer that for you gives you the best representation of the material that you have.