10-speed cassettes are very closed spaced and pretty intolerant of "near miss" shifting so a wider spaced cassette should help. 8-speed would be best as it has the same spacing as 7-speed but offers one more cog.
The problem could be the shift levers still aren't tight enough and slip after a while but it could also be frame flex. You mention it usually occurs while under a lot of pedaling pressure particularly while standing which does indicate the rear triangle is flexing under the high chain tension. The 8-speed cassette will allow for more alignment slop but a stiffer frame is the only sure cure.