David R. Hassall WA5DJJ
That has all the indications that your power supply isn't giving you enough current for the transmitter. Another hint is to glue a 4-40 Nut to the crystal can of the 27MHz Crystal. What happens is the can temperature changes the crystal frequency abruptly. The nut glued on the top of the can changes its temperature profile and it quits Jittering. If you can find a better 5 Volt power supply that has about 2 amps regulated and glue the nut on the 27MHz crystal can in the oscillator board I think you too will have nice straight lines. I have similar pictures on my grabber of your signal. They were weak and with the noise and the wobble. I couldn't decode the call sign. So you are getting out. It is just very hard to read.
Good luck, If I can help further, Just ask.