I'm pretty sure my videos are 1440x1080 but with a pixel aspect ratio of 4/3 so effectively 1920x1080. The frame rate is 60i according to my camera. This is what ffmpeg says:

Input #0, mpegts, from '00107.MTS':
Duration: 00:00:33.53, start: 0.767000, bitrate: 15920 kb/s
Program 1
Stream #0.0[0x1011]: Video: h264, yuv420p, 1440x1080 [PAR 4:3 DAR 16:9], 59.94 tbr, 90k tbn, 59.94 tbc
Stream #0.1[0x1100]: Audio: ac3, 48000 Hz, stereo, s16, 256 kb/s

So anyways, I have tried using the "HDV 1440x1080 60i" video profile in kdenlive, just using "Auto" under "Scanning" options and when I render/export to any format, the video seems to plow ahead of the audio at maybe twice the speed.

Am I using the wrong project profile? Should I change my render settings?

A script I was using before to convert the videos using mencoder had these options:

-fps 120 -ofps 60

I think ofps is "original fps". So it's saying the original is 60 and the new should be 120?

Try HDV 1440x1080 60i

Thanks but, that is what I tried.

I have the same camera and use "HD 1080i 60Hz" profile, everything seems to look okay and be in sync.