Yes, Treis Karden is further from Burg Eltz than Moselkern, but if you wanted to book a taxi, there is a company in Treis-Karden. Small town, so you should arrange in advance.
Another trick to still use a Rheinland Pfalz ticket and leave a little earlier. There is a regional train leaving Bonn Hbf at 8:57 that will get you there by 10:33 after connection in Koblenz. The R-P ticket is not valid until 9:00 am, but you can buy 2 VRS Preisstufe-1b tickets for 2.90 EUR each. These are valid to the Bonn UN Campus where the train stops at 9:00 am, so then the R-P ticket becomes valid. Of course, if you are not staying by the Hbf, you may also want to use those tickets to get from where ever you are in Bonn to the Hbf beforehand.