I can't say I've ever heard LEEP referred to as "experimental," and am not sure what the basis would be for such an opinion. LEEP is certainly a tried and true tool used in clinical practice, and is a common treatment option with cervical cell changes are removed.
Beyond LEEP, cervical dysplasia is often treated through freezing the affected area (known as cryotherapy). Another procedure, where a cone-shaped area of tissue is excised (and appropriately enough referred to as cone biopsy) is sometimes used, but not so much with CIN 1. Read more about treatment options at http://www.ashastd.org/hpv/hpv_learn_dysplasia.cfm#6
I wish there were more I could offer! Let us know how things work out, if you don't mind.