It kind of looks like you need more organic matter but you need to determine that with some more simple tests like these;
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. Your primary concern is the OM level and yours may be pretty good.

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.

Depending on what you want to grow your soil pH is heading toward too high, the best soil pH ranges between 6.2 and 6.8 for most plants. The term immediately available nutrients means little but that is all they can measure and more compost may well change those numbers, but it is long term nutrient availability that you need concern yourself about and that comes with sufficient levels of organic matter in your soil so the soil bacteria can provide that, and the low nitrates could simply be because your soil was too cold.
My soil is sand and it takes a ton of organic matter to fill in the pore spaces between the sand particles so enough moisture and nutrients are held in the plants root zone.

Thanks. So it sounds like, although it may take some time, adding compost will help with the nutrients as well as pH?

I've got a couple bags of organic humus & manure -- does that sound like a good start? Or should I grab something rich like "mushroom" compost or soil conditioner?

Absolutely. Compost is listed as a soil amendment and not a "fertilizer" because the nutrients in the compost are not readily available, they are very stable and are released for the plants as the plants need them.

bstwe: I would be concerned about the low trace minerals: iron, manganese, and zinc. Most produce in America is seriously short of potash, manganese, zinc, and iodine -- which is why many of us garden organically. They are all essential for plant and animal health; they control stuff like elements of the immune system.

Did your tester give you recommendations? If not, get a new tester. It's hard to know howw much iron, manganese, or zinc you should add without knowing the numbers on what you have. If your tester didn't give you the numbers, get a new tester. Don't go adding any trace minerals based on a qualitative test, with small trace levels you could easily go overboard and create toxicity. As in all gardening too much is worse that not enough. I guess a safer bet with trace minerals would be to add kelp meal or, absent that, granite meal at 5lbs. (kelp) and 1lb. (granite) per 100 sq. ft. (wild guesses).

As far as calcium, potash, and magnesium are concerned you need to know the percents (of base saturation) to know whether they are in balance -- because balance is everything and absolute levels have little significance, believe it or not. As you might surmise, there are optimum ranges for these percents.

Failing all this, compost and more compost, as others have said.

Regards, Peter