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I understand that you may want to spray Round-up on the lawn, but have you considered painting the seedlings individually. If you cut the seedling and you paint the cut, the seedlings will die. The alternative is to keep cutting them down. They will eventually run out of energy and die off.

To keep new ones from sprouting, consider adding a pre-emergent like Preen to your lawn regimen. It will keep the aspens from sprouting and will help keep weeds down as well.

I would treat the area with some fungicide to keep out diseases, but other than that, I would leave it alone. The tree will heal over better and faster if the wound is left open to heal itself. As long as the bark is not removed all the way around, the tree can recover fine.

Here is more information:
https://www.gardeningknowhow.com/ornamental/trees/tgen/repairing-tree-bark-damage.htm

These articles should help: https://www.gardeningknowhow.com/plant-problems/pests/deer/how-to-protect-trees-from-deer.htm

https://www.gardeningknowhow.com/ornamental/trees/tgen/repairing-tree-bark-damage.htm

You forgot to upload the photo but let me give this my best shot. This could be a poplar borer infestation. I would review the following article and if you agree, follow one of the recommended control options:
https://www.colostate.edu/Dept/CoopExt/4dmg/Pests/popborer.htm

The brown buds sound as if they are damaged, perhaps by a late cold front. I would snip off the dead growth so that new growth can come through. For additional help with non-leafing of trees, this article has more information: https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-leafing-problems.htm

Removal of an Aspen tree and its seedlings is not easy task.

Here are a couple of links for you.

http://extension.usu.edu/htm/news/articleID=2261
https://www.colostate.edu/Depts/CoopExt/4DMG/Trees/aspencan.htm