Sooo, About That Straw Cover...

[Dirtmechanic]

I think you will use a better tiller more than 1x/year. The Mantis is a real fro-fro machine, IMHO. In fact, if you till so that the soil looks like coffee grounds and it isn't amended with compost, it will dry hard as UNamended clay. I have seen this, so I till IN my compost.
Tilling doesn't remove using your shovel and use should always mulch around your vegetables, too. When I fix my flower beds I need to shovel the sides bc they are compacted.
I am surprised that I haven't broken mine! It is this model (I think, since I have owned it for at least 15 years now):
https://www.walmart.com/ip/Bronco-R...hguid=841ef6db-519-16876abd03214a&athena=true
I love tilling, just like I love mowing!
If I were working on your clay, I would shovel up the clay into big clods and then till it, then go over it again and till in compost.
I need to pull out the "Peck N Play" and put my chickens out this year to work on the squash bugs!
You can also till your compost pile and help it break down faster. I use medium pine shavings in my chicken's coop and those shavings takes YEARS to break down.
@bobm cats are your solution. Plant some catnip!! Why feed your own kitties when your neighbors will share!! Haven't MET a cat Yet who understands property lines.

Fellow Troy-bilt fan! I drive a super bronco about the patch myself! Really makes life easier in this clay. I like a front tine tiller too, but for thinner lighter work like weeding. I mainly use a stihl tiller for that stuff, it is not very wide or digs to deep so it is great for details.

 

[Beekissed]

We've always had Troy Bilts as well but prefer a rear tine tiller. Sold our last one when we switched to BTE, though. The only thing we kept was that Mantis for some light fluffing of the mulch if needed.