Dsper, in order to get the attributes you mentioned, it will require more than just an amp.
No matter what amp you use with a resolving speaker like Maggie's (and many others), you need to have a good source to deliver those attributes. Any source with a cheap opamp output stage will sabotage even the most optimal amp/speaker combo.
I haven't heard any Dacs under $2k that I think are worth pairing with a 3.7. I'm sure there are some out there, but the lowest I would go (and actually one of the best) is the NAD M51. Cost no object, I would go with the Wadia 321 or any ARC DAC model 3 or greater. They give the perfect combination of detail, warmth, and analog flavor.
Also, if you want a "warm" and more dynamic sound, I recommend using subwoofers with Maggies. Yes...I used plural because I never recommend just getting 1 sub and sticking it in the corner. You could buy 2 small REL subs for less than $2k total. I guarantee it will have 100 times greater impact on your system than wasting $2k on cables.
As for amp recommendations, you have countless options if you use autoformers like I mentioned in my previous post. McIntosh is a surprisingly good match because autoformers come with their SS amps and they are very reliable/powerful amps that can easily drive the Maggie's properly.
On a budget, I'm a big fan of the used McCormack amps. I usually get them modified to cost-no-object SOTA performance, but even in stock form, they will give you a liquid yet dynamic sound from the Maggies (assuming a good source). BTW, if you get the small used McCormacks, I think it is worthwhile to at least get the Plitron transformer upgrade from Steve McCormack if you're going to use them with Maggies.
Magtech's are fine, but they are a niche type amp and wouldn't be something I'd recommend in general.
If you're on a super tight budget, don't let all the Emotiva haters sway you from their products. I've tried several of their amps and they are definitely capable products for the money. I would stick to the bigger ones though with Maggie's.
Parasound is another tier in the budget range that produces quality amps that work well with Maggies.
If you ever want tube sound and cost-no-object, I would get ARC reference level amps.
That's about all I can recommend based on personal experience.