Yes, grovelly makes sense. "In a text"? In a book: it should be printed correctly, but in casual writing I keep coming across adverbs like "radicaly" so spelt.

I suppose you could argue that the suffix wasn't the adjectival -ly of "slovenly", "cowardly", but the more common -y of "teary, snowy, dusty"; in which case it might come under the UK/US distinction of travelling vs traveling. It's hard to tell because L is the only letter where the distinction is clearly observed.

Can we find examples with another letter? Do we write fidgety or fidgetty? Crotchety or crotchetty? I think I'd go for double T, which shows that -y does invoke the same rule, but are there any clearer examples? Do Americans use single T in these?

We want unstressed syllables ending in -p to match worship(p)ing, or -s to match focus(s)ing, or -t to match rivet(t)ing.