Hi Jimmy,
I think I've had a bit of success in calibrating this data, but it does require using the technique I describe in the calibrator database documentation. The concept is that you first calibrate without consideration of the spectral index, so making the assumption that the average flux densities of the two bands will calibrate to be very close to the correct value, then using that to determine the spectral index, then calibrating again with that assumed model.
In this case, we can calibrate 1253-055 as normal (you should start with an uncalibrated dataset, and I use 93000 below but everything should be done for both frequencies):
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mfcal vis=1253-055.93000 refant=2 interval=0.1
Then copy this to Mars and bootstrap the flux density scale:
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gpcopy vis=1253-055.93000 out=mars.93000
mfboot vis=mars.93000,1253-055.93000 "select=source(mars),-ant(1)" mode=scalar options=nospec clip=0.5
I excluded antenna 1 from the boot because the baselines that included it were responsible for those higher-than-expected fluxes in your mfboot plots. This is what my plot looks like from 93 GHz:

- mfboot.93000.png (6.75 KiB) Viewed 994 times
With that done, we can measure the flux model for 1253-055:
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uvfmeas "vis=1253-055.*" stokes=i order=1 options=log,plotvec,mfflux
I get a flux density model of 13.6337 Jy @ 93 GHz and a spectral index of 1.3597. Here's what the first round calibration looks like.

- round1_1253-055.png (10.87 KiB) Viewed 994 times
We can now redo the calibration. Again, from an uncalibrated stage:
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mfcal vis=1253-055.93000 refant=2 interval=0.1 flux=13.6337,93.0,1.3597
gpcal vis=1253-055.93000 refant=2 interval=0.1 flux=13.6337 spec=93.0,1.3597
This gives the result:

- round2_1253-055.png (10.83 KiB) Viewed 994 times
Which is much better, but not much good unless we can also get a good result using this calibration. So let's see what happens with the gain calibrator:
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gpcopy vis=1253-055.93000 out=j1534-5351.93000
gpcal vis=j1534-5351.93000 refant=2 options=xyvary,qusolve interval=0.1
gpboot vis=j1534-5351.93000 cal=1253-055.93000
This gives us:

- round2_j1534-5351.png (12.3 KiB) Viewed 994 times
Which looks pretty good to me. What do you think?