People generally don’t date to do Chesed, for that there are many other outlets. a marriage partner should be the person you feel most connected to, and can therefore build the most productive relationship that you can. Many people feel that the life experiences of a ger don’t mirror their own, and they won’t be able to have that same relationship. To think that this implies some put- down to the enormous respect that such people toward geirim is simply inaccurate.
That being said, it is entirely possible that a ger with a uniquely refined character could have more in common with a fine person than someone of similar backgruond but dissimilar ideals.
Yishai the father of Dovid, possibely the greatest Miyuchas of his time, married off his daughter to a ger who displayed a unique penchant for following truth.
Ps Willie is right that you may find a BT more receptive to the idea (they also have more similar backgrounds, being that they both discovered the truth by dint of their searching) Also, try the YU community, many of them are fine people, often without misgivings about dateing a ger.