I know from first-hand experience the Flex & Anan radios work quite well on AM transmit (much better than any modern knobbed HF transceiver) in terms of being able to reach 100% + modulation. Anyone tried one of the SunSDRs? They've got a QRP model 5-8 watts that looks interesting and is under $1k. While I also enjoy fiddling with SSB, I'm a CB'er at heart and usually won't hang on to a radio that can't do AM well too.
https://www.gigaparts.com/sunsdr2-qrp-transceiver.html
https://www.gigaparts.com/sunsdr2-qrp-transceiver.html