Yes, switch to Neocate (where I am that requires a prescription, although I know that WIC can give it out and if you qualify for WIC, you should see about getting it through them).
It will take awhile for you to relactate - and it will require a very supportive LC. Meanwhile, put your babe on Neocate.
With dd1, I had to use Neocate for awhile - long story - my supply had dropped to 10 oz/day and we rebuilt my supply while giving Neocate. Dd1 could not tolerate the regular hypo formulas. But when we got her back to 100% my milk (elimination diet - we eliminated dairy/soy/egg/wheat/legumes/peanuts/treenuts/fish/shellfish, she had multiple severe food allergies as an infant) - she gained better and did better.
It sounds like your Ped is skeptical of things - if he thinks the Alimentum is fine, ask for a stool test. They can test very quickly to see whether there is blood in your baby's stool, which is a classic clinical sign of food allergy. And if he's the one who told you that elimination diets aren't as effective as elemental or hypo formulas, it's because he doesn't trust you as a mother (and likely any other mother either) to follow the diet carefully. The research shows that full elimination with breastfeeding is best, if it is at all possible for the mother.
Good luck with relactating! What helped me, while rebuilding my supply, was
A good LC - follow her advice!
A supportive family (husband and my family) and coworkers (tell them what you need them to do!)
Hospital grade pump
Mother's Milk Tea
Oatmeal, oatmeal, oatmeal
Getting more sleep
And, believe it or not, I found that my supply seemed better after dh and I had been intimate. So -- maybe something to try?