Es gibt Minipumpenhalter, die direkt an den Befestigungspunkten des Flaschenhalters unter dem Käfig befestigt werden und die Pumpe an einer Seite der Flasche halten. Ich habe einen mit langen Schlitzen für die Käfigschrauben, mit denen der Halter weiter von der Mittellinie des Rahmens entfernt montiert werden kann und breite Rohre aufnehmen kann.

Sie können auch versuchen, Ihren Pumpenhalter am Sitzrohr oder Oberrohr zu montieren.

Here's a "mini floor pump" which can be strapped on pretty-much anywhere on the bike that is out of your way.

(Please disregard the battery under the velcro and temporary wiring wrap.)

That holder is designed to sit on top of two bottle mounts, rather than off to the side. So its a thin flattish mount on the back rather than being designed to sit off to the side. Better photos on the reseller's site.

There are no rivnuts on that bike so I used the two provided cable ties. They seem fine so far.

If you're okay to buy a new pump, what about a frame pump? As pictured, they wedge into a corner of your frame and run parallel to the top or seat post.

Downside, they're not very popular for aesthetic reasons, and your full-suspension bike has fewer places it could go. Perhaps under the top tube?

Would fixing the pump mount with a couple of hose clamps be a solution for you?

And by hose clamps I mean those devices:

Remember to use some electrical insulation tape to protect the paint on your frame and measure the perimeter of your frame to pick the correct size of the hose clamp.

If the clamps shown above won't please your aesthetics, there are other models, like those: