Indeed there are other places to send soil samples for analysis. There are many independent labs around the country and I've been using logan labs. I think their tests are affordable, and provide sufficient information to make soil amending decisions. https://loganlabs.com
The best place is the same place as last time. If you are going for measurements over time. Labs can have slightly different procedures that can throw off comparisons a bit, but any good lab will be dedicated to their own procedures being consistent.
Standard soil tests are a good measuring stick, but there can be a lot they don't show once you get into soil biology crop interactions. There's other tests for that, and sap analysis. I'd pick whatever soil test lab is nearby.
I personally like using my local county extension office as besides usually being the cheapest in cost BUT not because of cheap testing methods, I also like that they KNOW the area and some even give more in depth explanations of what you need and why than just a generic test. As an example I've looked at the tests from a few states and they may all say you need calcium for example but instead of just saying you need 2000 lbs per acre they explain that in the northern part of that state the soil is more alkaline and the low pH you have is probably more caused by overuse of (N) or other amendments that lowered the pH, NOT a low amount of (Ca) while others in the mid state area only need to add 1500 lbs per acre while the southern part may need the full 2000 lbs. This is because the local state schools have only looked at soil in their region while generic tests are nation wide coverage of these nutrients NOT a local look. Besides they also have answered many of my questions about many different topics beside just soil tests. Because of them being local they can answer things such as when in my area is stinkbugs a problem, organic and regular prevention methods etc. When to plant or even can I plant this crop or not in this area. I personally am in South Mississippi and live in zone 8b and use Mississippi State University (local county extension office) at least 4-5 times a year and when I first started farming it was almost a weekly visit... IF you are having a problem with the office in your county you might look into going to a neighboring county and talk with them and see if its just a personal problem. Then get their phone number and you can use them instead. My local one is great and I even send em pictures on my phone of odd questions like "what is this weed in my field?" or "what is this bug?" "is it a good bug or bad bug?". He usually answers within an hr. except one time and he was like "I'm so sorry, I was in a meeting with my boss" but he still answered me the same day.