So if you don't want to go the PS eval route, you can look for an SLP in private practice who specializes in young kids, and there will likely be much less waiting time. Look one up online through ASHA (American Speech Language Hearing Association), or just in your phone book. If that doesn't work, try to speak to an actual SLP at your local hospital or State Early intervention department, they can probably give you the name of an SLP to call.
That being said, R and TH are usually not addressed formally in preschool because they may come in on their own sometime before age 8. Now TH is not very hard to teach (compared to other sounds), because you can look in the mirror and see that you need your tongue sticking out between your teeth just a little bit. A 3yo may have difficulty doing that instead of F, even in front of a mirror. Try it out in a playful way, but if it's frustrating, don't push it. Point out the sound when you read aloud to her, and if you can deliberately pick books with TH words to read to her, it will help her to hear the sounds often. If you have any phonics materials around, that's a good place to find pictures of TH words. And teach the two TH sounds separately (THing vs THat - you need your voice box turned on for the second one) Early phonics readers at the library are good as well. I did that with my son when we started to do phonics around 4.5yo with TH and L. He's improved a lot in 2 years, but we're still reminding him
Saying cown for crown is an example of "consonant cluster simplification", where one or more of the sounds in a blend is omitted, and that is very typical of 3yos. You can highlight the sound in "grrr" when playing and see if she can copy you. R is a challenging sound in general because it is made completely inside the mouth, so you can't see it, and it's made a bit differently depending on what vowels are nearby in the word. You have to be able to follow very specific directions to work on it, so it's usually only addressed informally until age 8 or so. Can she make an R at all, or does she just leave it out of blends?
My 3-almost 4yo dd sounds similar. Same errors, as well as leaving S out of blends and saying W for R and L. All "normal" errors for her age, but I am constantly translating for dh as well as strangers...I worked with her a bit on adding S back in to words like snake, snack, stick etc, but everything else has been informal: reading S books to her, repeating words that she mispronounces back to her correctly in conversation (ex."Dat's a reawy big fing" "Yes, THat is a huge THing, you're right!" Hope that helps some!
) just had her annual physical. I mentioned to the pediatrician that she has trouble with the r and th sounds, saying cown for crown and fing for thing and that my husband has more difficulty understanding her than he did our son at that age. (I will note that my husband has a 70% hearing loss in both ears for which he wears hearing aids.) The pediatrician immediately recommended we get her a speech evaluation, as his stance is that it's better to seek an eval. when nothing is wrong than not to seek one when there is a need. (He also mentioned that it's our tax dollars, so why not! 
I'm so sorry for what you went through, but thank you for sharing your experience.
PMing you to continue the discussion