Mark, generally its better to understand what we wish the plant to do with the fertilizer.
The area under the tree will of couse be somewhat drier owing to the tree's taking what it wants.
There is ample shade under a linden (littleaf linden)...as they say, unter der linden--that famous street in Berlin)
due to the branches hanging low. I had so much of it on my linden I had to resort to cutting to get any kind of sunlight to the lawn there.
So its a perfect spot for the hosta and astilbe--shade lovers.
Now I don't believe hosta is a flower producer enough to be concerned about---yes, even tho they do flower.
Astilbe is a decent flower producer. I think being in shade with some sun is sufficient to make it bloom half decent.
In such cases, I prefer to give a 20/20/20 foliage feed to these two while I still try to encourage a lawn by feeding it a higher nitrogen fertilizer ...but keeping it well away from the plants.
Too much nitrogen will prevent flowering--how much in these two cases, I have no idea but I prefer to at least give the flowering plants a chance.

If you intend to have grass in the vicinity of the tree's underbranching, then you can give it something by way of a granular 24/6/12...21/7/7.....and give the plants a 15/30/15...to encourage bloom. After bloom, I would suggest the 20/20/20 to encourage new growth of foliage.

There are less potent fertilizers...10/10/10...5/10/10...but they are specialty feeds designed to not overload the soil where it matters.
With proper watering and sufficient sunlight, the amount of fertilizer can be less.
In this case, if you prefer, instead of the fertilizer in spring, wait until growth is seen and give it compost in lieu of. The lawns, keep giving it high nitrogen -- at least 3 times in the season...but keep it away from the plants and garden.

Your hostas just need more light and plenty of water to grow well. They are not shade lovers, but shade tolerant, preferring morning sun and bright shade to dense shade. Can you limb up your trees?

What does a good, reliable soil test say about the nutrients in the soil now? Never, ever simply spread some kind of fertilizer around without knowing what is there now and what needs to be added, if anything. Contact your local office of the Cornell University USDA Cooperative Extension Office about having that done and then dig in with these simple soil tests to learn more about the soil you have,

1. Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. A good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer you soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.
and what needs to be done to make that soil into a good, healthy soil that wil lgrow strong and healthy plants.

Here is a link that might be useful: Cornell CES

Planting further out from under your Lindens will produce better plants, as the Lindens will take what they need first. As far as the fertilizer goes, I would recommend using compost around your plants and worked into the soil. Compost is packed full of many nutrients your plants need. Not just NPK. A good organic fertilizer will also do the trick. An organic fertilizer usually needs to be applied less frequently than a chemical based fertilizer and also has things like trace minerals, calcium or microbes for a better balanced soil. If you like a liquid fertilizer, Merrill's compost tea is fantastic, if you would rather use a granular formula, Milorganite or Cocka-doodle-doo are good choices.

Here is a link that might be useful: organic fertilizer