I'm an ordained minister!

[bluebooger]

...
Not only is this a problem for those wanting a secular marriage ...

how is it a problem for people wanting a secular marriage ?
why would anybody wanting a secular marriage go to an ordained minister ?

...
... It's also a problem for people who live in rural or less religiously diverse areas and can't find an officiant of the domination/religion of their choosing.

if their preference is to have their wedding officiated by a minister from their own domination and they can't find one what makes you think they'd choose a minister from the Universal Life Church ?
the whole point is they what one from their own denomination

...
People shouldn't be forced to choose to have their marriage officiated by a judge with whom they have no personal connection.

why not ?
you get your children delivered by doctors and nurses you have no personal connection with
you probably don't have a personal connection with your accountant or lawyer (and I guarantee each person's accountant and lawyer is more important than their minister in most marriages)