I like hill climbing. I'll even do shorter, very steep hills for the challenge.

My 11-32 is really nice, I won't switch back to the 11-28. I even use the 34F-32R low gear on moderate hills, spinning at 90 rpm. And I can stay seated on 10% grades now, instead of having to stand up.

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Many riders report that a 11-32 works with their existing derailleur.
The 11-32 worked fine with my Ultegra Di2, which was supposed to have a 28 upper limit. There's not much gap between the top pulley and the 32 cog, but it shifts fine.

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equipment changes:
The Wolf Tooth derailleur hanger is a little longer, to move the derailleur pulley away from the big cog. I've never tried it.

A longer cage derailleur allows for more chain wrap, to keep from completely folding up the derailleur arm in the small chainring - small cog combination. (But that's not too critical, the small-small is rarely used, and the chain might just rub a little between the returning chain and the wrap around the top pulley, annoying but not a huge problem.)

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Try the cassette:
Install the 11-32, keep the same chain.
With the bike off the ground on a repair stand,
Shift to a middle cog.
Shift the front to the big chain ring.

Now, carefully shift to the 32 cog. Don't force it!

1. You must have at least a small jog in the chain line at the two pulleys, the derailleur arm can't be stretched straight out, or you'll jam the chain. If so, the chain is too short, and you'll need a new chain.

2. How close is the top pulley to the 32 cog? There has to be at least a small gap to let the chain shift on and off the cog. If it appears to work, try shifting up and down to verify, and test it with the small chainring too. Then do a careful, short test ride.

3. test the small front - small rear combination. The derailleur arm will be folded up most of the way. But if the returning chain from the front chainring is sagging and slack, that's not good. It's very unlikely, though.