You're cute with all your dickery and condescension. The grasshopper recommendation was appreciated, and if Grasshopper had a presence closer I would chase it down. Truth is, I just don't have time to run 55 miles for parts and service. It's not a choice. It's my demanding full time job, landlording my other properties, children, dogs, chickens, taking care of the acreage, flipping houses in between it all, and living in an area that has horrible traffic so those 55 miles could end up taking 3 hours each way. I used to have 10 hours to go with the landlord and pick something up. Unfortunately those times are gone.
Grasshopper looks like a good fit. It's weird they don't have a dealer near me, usually I put in my zip code and have a choice of 5-6 places to go. I have 6 gravely dealers within 15 miles, 4 Kubota dealers within 20 miles, 5 Exmark dealers within 15 miles, and 4 Walker dealers within 15 miles. Perhaps I should have added that there will be times when I won't be servicing myself. One more item in my "great long list of things that are difficult to get at my price level". The walkers also have front decks and I've spoken to my dealer in the past but he felt like it's a bad fit due to inclines and potential spring wetness.
I'm avoiding going into the dealerships due to covid-19 so trying to get a bit more info online first. However, search engines are cluttered with bad recommendations that only include affiliate links.
As far as budget goes I felt 10k for a personal mower would be ample but maybe I need to be persuaded to reach deeper into my pockets.
I think it is called life.
One of the things Americans have a big trouble with down here is our plain talking, so if you found my tone offensive it was not meant to be but we don't tippy toe around things here.
Sydney is 55 miles north to south
A trip from Cronulla to Palm Beach will take around 10 hours so don't use traffic as an excuse.
I am 50 miles from the center of Sydney and it can easy be a 3 to 4 hour drive both ways, I know what heavy traffic is like.
There is a funny sort of mentality I see here a lot that because a person wants something it has to be available locally easily & cheaply and that is rarely true anywhere.
Getting a single mower to do what you want to do efficiently & quickly is a really big ask.
For starters vertical shaft engine are not supposed to be used on slopes.
This is because the sumps are wide & shallow so it is very easy to end up with the oil pump intake screen out of the oil.
You have 2 to 3 minutes of that before the engine goes bang big time.
The most common engine rebuilds I do is for this reason.
There are 3 of them in the shop right now waiting for me to feel well enough to pull them apart.
However we don't know how steep your hills are and how big they are so a mower with a horizontal engine would be my number 1 priority .
Then there is the soft ride requirement
The most common ask of ZTR customers is to bypass the seat switch because they bounce around so much the engine is forever cutting out.
This is an inherient design problem because of the way the weight is distributed so the better brands fit a seat switch delay and having one of those would be the number 1 criteria if you go for a normal ZTR
Out front ZTR's have a better weight distribution and do not bounce around as much .
As you state you have a shinny bum type of job, I would suggest a stander so you are using a different set of muscles when mowing and relieving the pressure on your lower back
Standers are also much more agile than sitters so there is a double bonus there getting around the tight garden beds .
Keep your old mower and get a tow behind vacuum for it to remove the leaves .
FWISW I am on a small corner of a 1000 acre farm, in the old farm house.
The landlord has 5 old tractors ( inters ) each one is set up to do a single job and do that job well.
For the past 15 years we have been mowing the entire farm three times a year using Cub Cadets ( the good ones with horizontal Kohlers ) and would be continuing to do this except most deck parts are NLA and they are all well over 10,000 hours so are getting a bit worn out.
Thus the 2 Kubotas
An up front diesel Kubota would also do the job you want but again adding a bagger for the leaves will defeat the benefits.
As you mow probably 20 to 30 times a year concentrate on making that as quick as possible & accept that the leaf clean up in fall will just take longer. or just get some one else to come in 2 or 3 times a year to clean them up