Have you tried having a consistent nap routine that is the same every day? I used to just let my daugher nod off whenever she felt like it and it seemed she rarely napped or didn't nap for long. Once I started doing the same routine that we use for night time but during the day, she'd got to sleep much faster and would stay asleep for longer periods. I still don't get the 2-3 hour naps like some babies give thier moms, but I usually get at least an hour to 1.5 hours.
My routine is to swaddle my DD (yes, we still swaddle at nearly 6 months), rock her in her dark quiet room w/ the air conditioner providing white noise, and sometimes give her my finger to suck on. Oh, and "Hush Little Baby" is also usually thrown in there...
My baby is younger (4.5 months, and probably weighs less.. 16 lbs) than yours, but napping in the wrap is what we're doing now.
When she stopped napping on her own and I realized I was spending all my days trying to get her to sleep, or stressing out (or being really pissed off and/or frantic) that she wouldn't go to sleep, I tried it and it worked.
For us, it is working great because I can still do things (not clean the whole house, but a few chores here and there, plus eating and typing and all that good stuff) and it is more comfortable/easier on my body than sleeping in arms. Also, it takes her *a lot* less time to go to sleep (from 40 min to about 10 min now) so I actually end up with less strain on my body from holding her, rocking her, bouncing with her in my arms.
I was worried (and still am a bit) that she would get so used to sleeping in the wrap that she wouldn't sleep elsewhere. So far that hasn't been the case. She is actually sleeping better at night due (I think) to resting more during the day. She still falls asleep in the car, and in dad's arms. And, now that her non-napping phase *seems* to be passing (at least for this time around) I can actually set her down sometimes and get 45-60 min. more nap.
I think I would try a PP suggestion of trying a regular "schedule" for naptimes. It has worked really well for me, too. My babe used to want to cat-nap for 25 minutes at a time 4-5 times per day. I started using a nap routine of nursing and rocking twice per day. He now naps once in the morning and once in the afternoon, on average for 2 hours each time. Good luck!