Ok see.... it helped. Now that we have some trust, given that the advice was correct...please do the rest.
Now that you replaced the capacitor, and touched up some solder joints around the VCO (yes, VCO,voltage controlled oscillator, not VFO) REPLACE the 10.240Mhz crystal. The advice I gave was meant to be done in completeness. Not to be a stinker, but there are reasons for this. Your problem will go from being there, to where it's at now, which is "mostly gone" to completely gone.
While you're at it, if you want, and have a decent multimeter that reads current in the ma range, we can help you adjust the bias and make a couple simple resistor changes on the transmitter as well so that it doesn't go negative during SSB speech peaks as well. It will clean it up as far as how it sounds on the air.