To be honest, Eurail is a rip-off for optional reservations to/from/via/in Germany (8€ per person and train) and I'd advise to use the DB website instead (click on "Seat only”; 4€ per person and journey).

But DB can't book any reservation either:

It looks like the Amsterdam - Frankfurt leg is already fully booked.

Just checked-and it seems there are 2 reasons; again some works along that line AND the end of the Easter hols for many or perhaps a big group who took some cars-strangely even bahn gives an ALtern via Paris (avoid that=expensive Thalys and then even more expensive INtern TGV), plus change in Paris via metro).

This means either change (many) more times or change date  (but if its works, it will also be on the sunday-end that will be even more busy).NOte that on all these DB=german trains the REServ is NOT mandatory-but you run the risk of having to stand-not the whole route though. REServed seats lapse after 15 mins and if the booker did not turn up-you can use it. Happens fairly often.

IF you have more time and want to have some nice views: take the old line along the Rhine south from KÖln (Cologne) and not via FRAnkfurt, but Mainz-Mannheim_Karlsruhe-Basel-Swiss-on this line there are also hourly IC-trains. The direct trains use the superfast line (mostly soundscreens) KÖln-FRA.