It's pretty likely that a 32 will fit. I have 11 speed Shimano now, and the 11-32 is way out of range of the manufacturer's specs. It works fine on my bike.
I googled and found this
old thread on 11-32. It did work for the rider's bike. Comment 4 reminds to make sure the chain fits the big-big combo -- test it on the bike stand with hand cranking. If the small-small lets the top pulley chain rub on the bottom chain, that's no big deal.
And this
weight weenies thread. It worked for them too.
When I was running 10 speed Campagnolo, the 12-29 was out of range for the derailleur, but almost everyone found that it worked fine.
I really the the 34F-32R low gear. I can stay seated on 10% grades, riding slowly at a quite low cadence, but the pedal pressure is moderate. I'm not "grinding" the low cadence. I keep the 11-32 on the bike all the time, unless I'm doing a long, very flat ride.
Sprocket size
From this
sprocket radius chart,
28 sprocket is 2.233 inches, 56.7 mm
29 sprocket is 2.31 inches, 58.7 mm
32 sprocket is 2.55 inches, 64.8mm. That's just 6 mm larger than a 29. Use a 5mm hex wrench as a gauge, is the gap between the top pulley and the sprocket bigger than that?