the gas tank does in fact come out but it's a pain in the butt! Don't take it out unless you want to exercise your right to almost completely disassemble the mower. Once the tank is out, you're not too far off of total disassembly....
take the wheels off. Use one hand to guide the belt over the pulley from the outside and the other hand from underneath to put the belt in the general location where it needs to be. Sometimes makes it a little easier.
LOTS easier on a lift. I don't know how many thousands of HST belts on the Z series I did, but 99% of them on a lift. I did mine at home while laying on the ground. No fun at all, in comparison.
The belt will fit in there, trust me. ASSuming you have the correct belt, of course. K3011-13560 or K3011-13561 I think. Some of the parts store belts are wider and won't quite fit, and they don't stay on either. The vee angle can be different too. Always use OEM belt.
Remove blade belt from the clutch. Remove belt guide(s) from idlers (you already did). Remove spring if it didn't already fall off. Remove pto clutch limiter bracket. unplug pto clutch wire and fish it through so it's just hanging underneath. Now put the belt around the crankshaft, between the pto clutch and the top pulley--don't put it on the upper engine pulley, that's the last step. Fish it around your hst pulleys first, then around the idlers. Put the spring on, should go on by hand. Now, grab a 14mm or 9/16 wrench (IIRC that is the size of the crankshaft bolt that holds the clutch on). With one hand, work the belt slightly over the engine pulley, and using the wrench, turn the pto clutch retaining bolt (which turns the engine/pulley) while you push the belt into it's groove. It kinda walks itself in if you do it right. Reinstall the guide/bracket. Reinstall the blade belt. Reinstall the blade belt guide if you took it off (and you should, if you have one--they don't all have it). Reinstall the clutch limiter bracket. Fish the wire up through the frame and plug it back in.