There is this thing called a lawnmower. They work astonishingly well on most truly nasty weeds. Dandelions aren't nasty.

Most places, you either mow or you weed.

i have a similar situation. I would skip the professionals. Just mow it, then lay cardboard and lots of free woodchips. If some of your weeds are tenacious perennials you could hand pull or dig them out first. But I really think the cardboard will do what the chemicals the professionals will use would would. The soil will of course retain a seed bsnk of weeds that will emerge as you disturb the mulch but drastically less so that you will be able to handle them until your groundcover takes over.

If your afraid of running a riding lawn mower down that hill I'd suggest you consider buying a used professional "walk behind mower" like an Exmark. A lot of professionals lease these for 3 years and then the leasing company sells them,. Yes. it's used but these machines are way overbuilt and will last you for many years. Look on eBay or Craig's list.

Mulch around the trunks to keep the mower and weed wacker from damaging the trees.

There are two advantages of the walk behind mowers. One is that you're not riding on it, you're walking behind the mower, the most common sizes are 36" and 48". the size makes short work of the job. There's also an attachment trailer like item that you can stand on but when you get to a part of the lawn where you need more caution you just step off and the machine keeps going.

2. The mower deck sticks out in front of the mower and you're at the extreme rear. So they are wonderful for getting under trees, bushes, etc. The machines are also very maneuverable, you can spin them on one drive wheel, which makes trimming even easier.

@John D Zn6a PIT Pa, thank you for the Exmark suggestion! We maintain our horse pastures with a lawn tractor but there are several areas where a pushmower is needed but its small size makes addressing them such a chore, we neglect them.

DH is going to love this idea! Happy Father's Day to him.