I don't know what, if anything you can do about the P and K being that high. For the pH, if it's that high because you or a previous owner over limed to raise the pH of a soil in an area where most soil is naturally acidic, it will probably start to go lower on its own.

If not, you can lower the pH using soil sulfur. If you do, you should dig it in where possible. It takes some time for it to take effect, but it's a fairly long lived change. It may take a lot to have much of an effect, so it's probably not practical on a lawn. In fact, I wouldn't do anything unless you have plants that are suffering from the high pH (for example, if some of the plants are showing signs of iron chlorosis--yellow leaves with green veins).

Adding lots of organic matter will help the soil buffer the high pH, so it won't affect the plants so much. Organic matter won't really acidify the soil, but ill help bring it closer to neutral.

Where are you?
Where was the soil test done?
That is not all that that soil test had, what did the rest tell you?

Add plenty of compost!

We live in zone 5. The test also showed we have 6.5% O.M. We try to keep an organic garden so anything that we added are things like bonemeal, alalfa meal, manure, leaves, etc... Our soil is finally black and crumbly, it looks like good soil. Before it was hard and clay-like.
Will my plants get burned or have problems? My tomatoes last year suffered puffiness. We have a very intense garden and we thought it should be depleted, I guess not, LOL.

Another question is if I should get my soil tested for nitrogen? -Or if I shouldn't even bother since everything else is high.

"Another question is if I should get my soil tested for nitrogen?"

Nitrogen is pretty transient, so you probably need to add it in one form or another on a fairly regular basis.

Nitrogen availability in the soil depends on soil temperatures, which influence that activity of the soil bacteria which provide the plants with Nitrogen. Soil Test Labs seldon test for N now because of that. With 6.5 percent OM you are in the optimal range, just keep adding OM to your soil to maintain that level and N should not be problematic.

You can run into problems with very high potassium levels. It will out compete' other nutrients in the soil resulting in plant deficiencies. Although I doubt you are anywhere close to running into such problems. High phosphorus is not a plant problem and is generally only a concern in that it can be an environmental problem. High pH adversely affects the solubility of various nutrients (and soil organisms) and can lead to deficiencies. What raises pH is potassium, calcium, magnesium, and sodium. If you have hard water (calcium and magnesium) over watering every so often will help in that it flushes some of the salts out of the root zone. I would guess that your garden will be fine. If you are adding a lot of compost (and an organic matter content of 6.5 says you are) you are likely to see your phosphorus and potassium levels continue to rise. These nutrients do not readily leach and are concentrated in the composting process. Typically nitrogen is not tested for because it is tricky to get an accurate test and as was said above is very transient in the soil.

My suspicion is that you, having an "aggressive" garden (your term, not mine) means that you add a 'balanced' fertilizer now and then, to force growth out of those vegetables, or even the lawn. Well, you're doing what everybody has been told. Can't blame you for that.

But it's not right. Not anymore. Not for you. You have graduated to the category of 'agricultural producer' rather than 'ignorant homeowner' or 'ignorant gardner'. And 'ignorant' does not mean 'stupid', rather it means 'not yet informed', which does not mean you will never be informed, it just means that you haven't been informed yet.

The fertilizer companies design, and blend, and then market their products to homeowners who are basically ignorant of the problems that you are faced with. I can't really fault them for that. Their typical customer (you might make a better list) has:
a. neglected their lawn for four years or more, or
b. graduated the kids from school, and there's nobody playing soccer out back anymore, or
c. bought a new house, in a subdivision that used to be a farmer's field, until the topsoil was scraped off, or
d. in the gardening field, started a garden, by rototilling up a patch of ground. They're going to go back to the store, next week, to figure out what they might grow. But at the time of tilling, they hadn't a clue.

No offense to those folks. We've all been there. The 'balanced' fertilizer that these folks purchase might be (pretty good chance, really) just exactly what they need, or, more likely, at least calculated to solve most of the problems ("please don't call us on the phone. Please don't.") that these folks are likely to run into.

But those 'balanced' products tend to have too much potash, and too much phosphorus. Those particular chemical components of fertilizer don't get used up, the way that Nitrogen does. On a subdivision lot, hey, phosphorus might be needed ("Throw in some phosphorus"). You are not on a subdivision lot. Nor do you need phosphorus. Nor potash.

But you've been adding it, faithfully, for years. Lucky you. But it's piling up, isn't it? The link below will illustrate how 'nitrogen only' will use up excess phosphorus by making things grow. Same is true (I presume) of the potash.

But you've got to switch to 'nitrogen only' for a couple of seasons, just to get the excess of the other two elements used up. Don't add anything else. Whatever it is, hey, you've got more than you need. I'm going to leave it to you to figure out what's most practical for your situation in the 'nitrogen only' department. It might be urea (my first thought), and it might not. I don't have your problems. I've got a few of my own.

And let's get to some good advice for you. I don't see any sense in your purchasing anything labeled 'Scotts', or anything labeled "Miracle Gro". Those things are designed (quite correctly) for my brother. He put some fertilizer down, about five years ago, and he might do it again, this year, if he thinks about it, because the neighbor made some comment (quite restrained, actually) about that lawn. And how we want this neighborhood to look. You know the rest.

Don't add anything to your garden. Whatever you need, hey, it's there, isn't it? Perhaps too much. Produce what it is that you're going to produce. After you produce it, do another soil test. Add what you need, and don't add what you don't need.

And let us know how it turns out.