Just my .02 ..
Grundig G6 - convenient, but audio amplifier noise is tiring. So much so that using the airbands without a squelch drove me nuts. Low pass filter didn't help much - that noise floor is still there.
Grundig G3 - BIG improvement, although a bit bassy. At least the audio amplifier noise floor is way down compared to G6. Overall ok, but would it be a major improvement over your Tecsun? Probably not.
Given your requirements, I'd actually suggest taking a look at the Grundig Satellite 750 if you have to buy new in that price range. The good thing is that I haven't seen any major faults with the QC, only the limitations of a sub $300 receiver.
750-BFO gripes - don't swing that thing too much! For USB, just set it to 12 oclock. Then use the main vfo knob lightly. Make *fine* adjustments to the bfo, that is no more than about 1/2 of a clock-tick for best sound. For LSB, set it to 1 oclock and go back to the main vfo. The BFO isn't really meant to be a wide fine-tune. If one uses it that way, they are bound to be disappointed with a lot of fiddling. If you go forward or reverse more than about one clock-tick on the bfo dial, go back to either 12 or 1 oclock position (depending on which sideband you are using) and use the main vfo to get on frequency.
Front end overload is controlled via the rf-gain, but given that you may not be using very large antennas, this may not be a major issue. Nice sensitivity and selectivity for what it is.