My info is from 2011 . . .
From Astrakhan you'll encounter a pontoon bridge . . . be careful. It's stainless steel and incredibly slippery for a 2-wheeler when wet.
The rest of the ride to Beyneu is best not done late. The roads have been deformed many places by the heat and heavy trucks. My KTM was fairly regularly airborne . . . it was reminiscent of the section of the ALCAN near Beaver Creek, YT. Funny watching Winnebagos get one wheel in the air !
Other than Lyoka (Leonid) in Beyneu . . . Astrakhan was wonderful and it's a long ride till something of real interest or significance (Nukus). Don't get bored and complacent !
There was a fuel stop about 30km before the UZ border. It's still present in Walter's incomparable waypoints. Stop there, even if you've gassed up at Beyneu. I encountered quite a scene at the border and without "insinuating" myself toward the front would have waited like many others (none on motorbikes) for several days in the desert unprotected.
Make sure you've filled your belly with water before departing Beyneu and that you have plenty of reserve.
At the border you'll need to do a three-step process for your vehicle check-in. English will not be present and you'll possibly be directed to the wrong window/kiosk/office several times. Previously, the Customs official sat in an unmarked office with blacked out windows on the RIGHT-HAND side of the main building toward the KZ side.
You'll not forget the wash board between Beyneu and the UZ border. Pay attention after the border for sand drifting SUDDENLY on the road. I met a German on a scooter (!) who'd required 3 days to come from Kungrad to Beyneu with two nites in the desert. "You have a race horse and I have a donkey." Hilarious and quite a bit of demonstrable pluck.
There's no reason to change money right after the border crossing. As the road moves toward Kungrad it will have some rollers. Several times there were police waiting for "speeders" with radar guns that were unattached to any power. Practice not noticing them.
At Kungrad benzine could become necessary to buy via bucket. Probably not but . . . welcome to UZ.
I think you've chosen a great path. Nukus and the Savitsky are fantastic and/or fantastically weird - a bit like eastern Europe pre-1989. And UZ is a bit like Burma but with a far less draconian govt. Do say "hello" to the 'Glorious Maximum Leader'.