Grass Chute for Liberty Z 48"?

I bought a Liberty Z 48" a little over a year ago and I love it. Only mow a little over an acre yard, but being in a neighborhood, I really want a bagger of some sort. I get really tired of throwing grass all over the street, my neighbor's driveway, etc. I looked at the Scag bagging system, but it requires a vacuum system and it costs over $1200. I'm not paying that much for a residential bagging system. Someone I know recommended a Grass Gobbler, or some other variation of a hard cage bagging system. I think these would work great for me, and they seem to go on and off very easily. Does anyone have any experience with these, and have a recommendation of which brand is the best, and what price I can expect to pay? Thanks in advance for your help.

I find that I can keep most grass out of places I don't want it by running 2 to 3 laps around perimeters going clockwise. Of course, there are exceptions. I believe the Grass Gobbler is a plastic grass catcher. I've never used one but do have an aluminium Accelerator one. They're well made, fairly light and durable with multiple sizes available and they can be expanded for leaves. Not cheap though.

I find side-mounted grass catchers to be clumsy and try to avoid using them, but I can justify having a powered rear bagger as a pro.

Ditto on the 2-3 clockwise passes.

There is a two bag mower deck air flow collection system for the Liberty Z. I have no idea how much it costs, but I do know that it is a fairly effective system and allows the machine to operate easily. The 3 bag blower driven collection system which is not available for the Liberty Z was $2,500 several years ago and probably more now.