Over the years I've read many posts from forum members regretting selling kit they really enjoyed, and that includes the Pioneer A400 and the Mission 752's. That's why ideally you must try any replacement in your own home.
I used to use an earlier model of the Rega Brio amp, but for me, there was a big jump in performance when I home demoed the Rega Elex-r. The current Brio may be great for you but only you can say really.
Like me, you seem to have owned your kit for a long time, so let's assume whatever you purchase will be with you again for a long time. Under those circumstances I would rather up my budget (or save a bit longer) and purchase something that is clearly a step up (or two), and something that you will not be itching to replace again anytime soon.
Also, it is worth exploring how a 'better' amp will improve the sound from your 752's.
Home demoing stuff does require a dealer relatively close to you, and of course usually limits you to purchasing new. The alternative is to keep researching (research the various brands/suggestions in this thread) and keep track of any local 2nd hand market. You may find you end up setting your sights on one or two items, and then if you are patient, one may come up. I probably spent nearly two years researching floorstanding speakers and another year tracking Spendors, before managing to get a pair 2nd hand. The wait was worth the effort for me as I will probably keep the D7's a very long time.
Also, I think if you get a 'better' amp (usually but not always, as they get more expensive you get more power (watts) that can drive/control speakers better) it will probably give you more options in the future if you decide to change your speakers too.