Jaggy Taggy wrote:
. . .
And my second thought was what is happening to the energy, since an SWR
gives me an indication of how much power reaches the antenna

It does not.

and how much is
either radiated from the feedline or lost as heat

It does not.

and here I have two
different SWR in the system, one at the antenna and one for the
antenna/feedline system.

I think it can't be that I would loose a whole lot at the antenna (high SWR)

The SWR has nothing to do with how much power is being lost.

but then wouldn't loose all that much for the system since the overall SWR
is lower.

The SWR has nothing to do with how much is lost.

Where do I go wrong??

In all the above. You need to go back and read again just what SWR is
and what it means.

Roy Lewallen, W7EL