Does prior oral HSV1 infection confer any protection from genital HSV2?

I have genital HSV2, rare recurrences (less than 1/yr) prior to suppression and no recurrences since starting on valtrex 1000 mg daily.  I know have had prior exposure to oral HSV via my exhusband's cold sores and to genital HSV1 from oral sex with him, but I never myself developed an oral lesion and I have never been tested for HSV1 or its antibodies.

My new love interest has oral HSV1, with somewhat frequent recurrences despite suppressive therapy.

We are wondering what the risk is to him of contracting oral or genital HSV2 from me with and without condom/dental dam use.

We are also wondering what the risk is to me of contracting genital HSV1 from him via oral sex.

We are mature adults and know that barrier protection is advisable, but we would like to know how the risks measure out with and without it...