I do in fact talk about this a lot; but it’s kind of spread out diffusely in other things I write (sometimes implicitly so). So I’m very glad you’ve opened up a discussion on it here in the Christian Living section. I hope other readers (as well as us guest authors) will use this section for discussions of practical devotion more often.
It’s hard for me to specify exactly from experience how UR per se has changed me: even when I wasn’t an apologist for it, I still have always had strong sympathy for it. So there isn’t a conversion-point difference for me. (Even when I did evangelism and apologetics before, I didn’t focus on hopeless damnation, mainly because I had my doubts about it. I did sometimes help defend other people’s attempts at non-universalism from specious criticism; which I still believe I’m obligated to do today, btw.)
There are many elements related to UR, however, which I began to take far more seriously in my life, once I began to be a more active proponent for UR.
One particular category of things along this line… I wish to God Above I could talk freely about. I can’t, for reasons I won’t go into. But the importance of self-sacrificial love became much more real in my life–including as a disciplinary process. (By which I mean discipline of myself.)
Other things I would rather not talk about because, as you suggested, I just don’t feel right about seeming to give myself compliments.
So, moving on to self-critical things (which I feel much better talking about 
), that becoming a proponent for UR has at least increased in me:
1.) acknowledging the absolute necessity of loving my enemies. Which also means, the absolute necessity of being fair to my enemies. I’m still not as good at this as I ought to be. But I do make strong efforts along this line. (Heck, I’d even rather call enemies “opponents” now. 
)
2.) a much stronger perception of my own sinfulness in need of correction and healing. (I don’t want this to be thought of as boasting, though. 
Wish we had a smiley for spitting. 
)
3.) relatedly, at least a moderately stronger tendency to overlook transgressions of other people (against myself especially).
4.) related to that, I try much harder to look for mitigating rationales and circumstances among people I disagree with (even vehemently ethically so). In fact, I’ve become far more conscious of the distinction between disagreeing with someone and disagreeing against someone.
5.) I appreciate the Old Testament a lot more now. 
6.) Since it was a vastly increased regard for orthodox trinitarianism that led directly to my active profession of universalism, there’s a sort of reflection back in that direction now, too. (When I consider orthodoxy, my appreciation of universalism increases; when I consider universalism, my appreciation of orthodoxy increases.)
7.) strongly related to that last one, my appreciation of God has increased dramatically. (Including my appreciation of the Holy Spirit, although I still want and need more exercise in that.)
8.) strongly related to both of the above, my desire for evangelism per se (not simply technical apologetics) as increased substantially; although paradoxically I’m much more unsure about what to do about that. (Hopefully a temporary problem; but, for example, I just don’t feel right giving to Lottie Moon or Annie Armstrong missions anymore. Even though I basically want to support them more.)
ick, I’m starting to trend into wanting to boast about some things. So I’ll change directions and add a comment similar to something else you mentioned.
9.) while this isn’t always true, my most (I have to put it this way, sorry…) irrationally hostile opponents in past years seem to have decided, for the most part, that I’m not worth their time seriously opposing anymore. They tend to get this way after they finally figure out (or remember–their memories tend to be problematic, let us say ) that I’m a universalist. I don’t consider this a compliment to myself; and frankly I don’t think it usually means they see theism per se (or even orthodox trinitarianism) in a better light. I’m simply not who they want to attack anymore.
However, there are other situations where opponents who can be very rational in discussion with me, but who didn’t know I was a universalist and so (understandably, as a first expectation) charged me with believing in hopeless condemnation, tended afterward to get very irrational in their continuations–probably due to annoyance at what they expected me to believe. (I mean that the emotional annoyance undermined their capabilities temporarily.) In those situations, once they learned I was a universalist, that problem just didn’t come up anymore; and I’ve been very gratified to have excellent conversations with them unimpeded by that problem. I don’t credit myself with that–but it’s a difference I’m very glad of, and it followed from my beginning to actively profess universalism.
Really, though, if I have to answer the question, “how should UR change us?”, the answer in principle ought to be: “loving God more”, “loving our sin less”, and “loving our enemy more, as our neighbor”.
And isn’t that what all the Law and the Prophets hang upon?
(That, and an increase in the belief that when all other things pass away these three shall be remaining: faith and hope and true love. And the greatest of these is love. One of the shortest tests I can think of for a belief about judgment, is: so, is hope remaining? 
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