Hi! I did this just last night! I had difficulty installing the chrome once the clips were attached to the door and the furry strip. Here's what worked for me.
First, the new clips were way too tight to fit over my door edge. I opened them up slightly with a chisel, inserting it in the central groove and tapping it in, on my workbench of course. The clip has a large groove in the middle and one 'clip on each side. The short 'clip' goes on the outside. The short side attaches to the inside upper part of your chrome trim. There's kind of a channel there, with a bottom ledge and a top one. Clips attach to the top one. Try them on your chrome trim before you install them on the door. If it's really hard to get them to bite on the chrome strip, open them up a bit with a chisel and a hammer. Not too much, otherwise the clip won't hold the chrome strip. If you open it up too much, smack it gently with a hammer and try the fit again.
Now here's the trick: first, press your clips onto your door edge, making sure you have the short 'clip' outside. You can use 4 or 5 clips per door. I have 4 one door and 5 on the other, because I had 9 in all, and both sides hold fine. Make sure your clips go down as far as possible, otherwise, if one is higher, everything will be out of whack. You can 'gently' tap them in place with a small hammer.
Once all your clips are installed, press your furry strip in place on the long 'clips' which are now inside your glass opening. Be careful not to bend your strip, and get it in equally on the clips by pressing down equally along your furry strip. Remember to put the 'fur' part on the glass side.
Once you've done this, place your chrome strip on the exterior 'clips' and press on the strip to get the 'clips to bite into it. Remember, the clips are bitting into the top part of the interior 'track' inside your chrome strip. The strip lays down at an angle, so you kind of push outwards. You may have to use some strong pressure to get it in. Watch that the ends of your door rubbers fit inside the spaces at both ends of your chrome strip. If rubber gets in the way, it will prevent you from pushing in the chrome strip unto it's clips.
WARNING! If you're tempted to use a hammer, even a soft one to 'help' you get your chrome strip in place, remember that your door is made of aluminium and is not that solid, especially at the extremities. It will cave in. Ask me how I know... Good strong hand pressure should get your chrome strip in place and you'll feel it fit in place. Look to make sure your chrome strip is aligned with the exterior 'clips' and that you,re not skipping one. If so, you'll have to pull your strip off and start over.
That's about as much as I can tell you. The secret is really to make sure the clips fit nice and tight, but not too much both on the door panel and on the chrome strip BEFORE installing it in the door. I undid my clips, chrome strip and furry strip 2 times before I understood that! Ask me if you need more details.
As I read your post again I notice you own a 250SL. My description is for a 1965 230Sl and I know MB changed the clips at one point. Don't know what clips you have. Photos available on previous post by 66andBlue where you see the difference