Based on the photos and some other Ask Extension Q&A's I've read, I'm don't think you are dealing with leaf miners.  They tend to leave more of of "white tunnel" type damage, whereas your photos show little holes with clean edges.  Here's an Ask Extension from two years ago that seems to be addressing your problem as well:

Camperdown Elm Tree infected with small insects #792633

Asked May 25, 2022, 3:26 PM EDT

I live in Ashland, Oregon and my Camperdown elm has small, 1/2 inch insects that fly and eat holes into the leaves, which then turn brown. Pictures are attached. I have just put a systemic around the trunk but was wondering if there is anything I could spray on the leaves to save them. They are full of small round holes and its all over the tree. Some of the leaves are turning brown and dying. The tree is infested with the insects. Thank You, Elizabeth Moore, <personal data hidden>. or <personal data hidden>

Jackson County Oregon

Expert Response

This is likely the leafminer sawfly. Adults are tiny, black, fly-like sawflies which can be seen on new foliage on sunny days. Small, legless leafminer larva feed between the layers of leaf epidermis, resulting in large brown blotches that gradually coalesce into one large mine consuming the entire leaf. Large trees may be completely defoliated; however, as new growth continues in May, the trees begin to leaf out at the branch tips and replace lost leaves with little apparent effect. On Camperdown elm, however, the mines do not coalesce and the dark blotches are visible on the leaves that remain on the tree.

These sawflies overwinter as pupae in the soil. As trees begin to leaf out, adults emerge from the soil and are seen as black specks on the leaves. They begin to lay eggs, at first, in the angles where the secondary vein meets the midrib. As the larvae feed and grow, the mines appear to coalesce. Mature larvae drop to the soil to pupate. There is only one generation per year.

Pest monitoring Look for the small black adults as leaves unfold in the spring. They are most active when it is sunny within the tree canopy. The little black adults are easily visible on the upper leaf surface. Sticky cards placed on the sunny side of the plant in early April to provide early warning that monitoring should begin.

Infested trees can be treated with systemic insecticide. Once damage is obvious, it is usually too late to treat for the season. However, if treatment it timed correctly, the condition is easily controlled. Young leaf miners live in the ground through the winter.

https://pnwhandbooks.org/insect/hort/landscape/hosts-pests-landscape-plants/elm-ulmus-elm-leafminer

Other possibilities are leaf beetles or leaf weevils. Check out this publication:

https://extension.colostate.edu/topic-areas/insects/elm-leaf-beetles-5-521-2/

Chris Rusch Replied May 26, 2022, 11:51 PM EDT

Hello,

Hi again, just consider the "leaf miner sawfly" as a "sawfly", I'd ignore the leaf miner reference because that is confusing.  Leaf miners leave dead, white tunnels in the foliage, not little holes.  

The Pacific Northwest Insect Management Handbook has the following information on controlling sawflies:

Cultural control - pick off any larvae you see (caterpillars), possibly hose off plants with a strong stream of water.  You could hang up yellow sticky traps to possible catch one of the little bugs for better identification.  

Biological control - insect predators include hemipterous sucking insects (for example, cicadas, leafhoppers, treehoppers, planthoppers, froghoppers, aphids, whiteflies, scale insects).

Chemical control for home use - applied as foliar spray you could try acephate, neem extract, carbaryl (Sevin), cyfluthrin, or spinosad.  

Because your tree is about 8' tall, you should be able to use an all-purpose ornamental contact insecticide and a hose end or pump-up sprayer.  

I would suggest going to a really good, well-stocked garden center and ask for their recommendations for contact sprays.  You could also ask about any systemic insecticides appropriate for ornamental trees.  In the past, there used to be a variety of water-in/drench type products, tablets that could be inserted into the cambium layer of the tree, as well as sprays.  I am not sure what is available these days.  One caution, systemic insecticides can harm beneficial insects such as honeybees, so my recollection is that systemic insectides have been gradually taken off the market.

Reading some on-line posts, one person's tree died the next year while another person's recovered and was fine.  If it was my tree, I would "baby it", care for it, spray it, water it, maybe fence it to keep away deer or mice from any further damage/stress, and wait and see.  Prune it in the late winter months then fertilize in early spring.  Rake up any fallen leaves from below the tree for good sanitation.  

Good luck!

Sorry for the late reply.

Best of luck nursing Seymour back to health!  I think that tree is in good hands.  Cindy Brown