Not too late. Since you mention snow, so your growing season hasn't even started yet. They will probably put in good growth this year, since last year was when you had just transplanted them. Bushes don't grow as dramatically fast as annual plants, but after each month passes by until next autumn, you'll realize the bush has been growing and fills in well.

When there is lack of funds, then you can just use the manual way. Get a hoe and start tilling the ground. When the grass reappears, pull them or hoe again.

Pruning to keep a certain shape, or just to remove the longish branches and make the plant look more even, will help if you want that. If you like the natural look, then just prune to keep the plant looking nice but don't need to worry about symmetry or shape.

Thank you!

Can I cover the grass with newspaper/cardbord to smother grass topping it with mulch? And I have some mushroom compost from last year. Should I put some around or near the shrubs? Or used coffee grinds? Lol sorry if this sounds silly!

You can start with covering the grass but I would also suggest to till it with a hoe, turning the ground. At that time, work in the compost . Then add the cardboard cover, and then mulch.
For the grinds, are you wanting them in as a soil additive or to stop slugs and snails? For the former, work it in also, and for the later, add it as top dressing.