I would not advise you to do so through speed-harvesting, because every sped hour costs TWO gems, and only give ONE acorn.
Ideally, as you are very low on gems, I also wouldn't do so through speed-breeding, as the speeding of breedings only "cost" gems and don't give acorns.
By far the ideal route for you is to speed-hatch, because 1 hour of speed hatched time = 1 acorn, AND you're "helping" your forest getting populated, which is good for the cash-flow.
I'm looking at your forest right now, and the solution for you is easy-peasy.
The most obvious choices are to first speed-hatch animals that you have in storage that don't require a new habitat to be built. As a general rule of thumb, I'd first speed-hatch whatever you have in terms of world event animals, as these animals can go nowhere else but in the special habitats that were made for them, hence, they're not conflicting with your normal hatching strategies for housing animals of more common animals that can go in the normal habitats.
Some candidates in your forest are (assuming you have all animals):
-Egypt: Ra, Sobek.
-Icecream: Neapolitiger.
-Autumn: Autumn Equifox.
Then, you can put 2 "nature-something" animals in that empty Nature Preserve you have on the lower green plots, you can also upgrade it to house 3 animals, next, you can upgrade the fire habitat next to it and house an additional fire-something animal there; you could of course also sell the Armordillo baby that's in it for an additional spot.
The above should already well cover it. If it doesn't, you can temporarily store some of the very abundant decoration you have around the den (and elsewhere in the forest) and put habitats there that are quick to construct. The fire and nature small habitats construct in only 10 seconds time and can house two animals each. And... if even that wouldn't be enough (which is not the case in your forest) you could temporarily sell the evolution flower and/or 1 or more farms and put habitats there....
Also: I see Halloween animals in your forest, but no Christmas, Valentine or Shamrock (unless I missed them). I'd expect you to have a good deal of that stuff in your storage. You can instantly place one or more of those habitats and then speed-hatch animals into that.
I'd go that route. From the amount of gems you mention having, you can probably only speed-hatch a few animals, so I'd focus on the coolest ones and/or special ones first. Personally I love the Egypt animals. If I were the owner of your forest, I'd start by speed-hatching the Ra and the Sobek (in that order). To be on the safe side: check the Wikia for the hatching times. The Ra is 22 hours from memory, so that's 22 gems to speed (and a 22 acorn income). If you do the math on the Wikia, I'm sure you can find a good solution.
Also, if there are some 2-4 gems left at the end, you could buy and speed-hatch Rock-Rhinos and/or a Frostfang. Finally, depending on the time you do this, and the animals you have in storage, suppose that after all this speeding you're still a little over 8 hours away from the end of the event, you could hatch one final animal without speeding, as long as its hatching time is a maximum of 8 hours.
Good luck! You can pull it off, I'm sure!