You will probably need to release tension on the cable but you can do that by shifting to the large chainwheel then downshifting without pedaling. That releases tension on the cable and lets you work the derailer. The chain will be on the large chainwheel and you’ll be able to see if you can move the derailer out anymore to get the clearance you need.

One note: Try this before doing anything to the limit screw. Adjusting the limit screw should be the very last thing on the list of adjustments on a bike. I’d put it on the list below cleaning the garage, doing my taxes, and/or getting a root canal. That’s how important “adjusting the limit screw” is…i.e. not very.

Is this a fairly new model of Shimano? Go to the Shimano tech doc site https://si.shimano.com/#/

Search for your particular DR model and then read and follow the appropriate DM for it. That'll start you at square one and if you follow it correctly your DR will work as it's supposed too. You might have to pull the DM for the shifter to get the instructions for the cable attachment and adjustment.

If that doesn't work, or the DM and other manuals are not understandable to you, then you need the help of a bike shop mechanic.

However you might just be a little too picky about noise. Some bikes are going to rub some when in the Big/Big or Small/Small combo. Usually that is bikes with 10 and 11 speed rears which I don't think yours is.

As a rule the deal with limit screws is you set up the outer so the chain is on the big ring smallest cog and the inside of the outer plate is a millimeter or two off the chain, and set the high limit so the derailleur won't go any further. Then shift to the small ring and biggest cog and set the inside of the inner plate 1, or 2 from the chain, lock it in place with the low limit screw, and never touch them again.

Unless your bottom bracket housing gets physically smaller .....

As for noise ... I am very picky about noise because I Know that there is a way to set up almost every bike to be noise-free. If you have a cheap bike and drive train, maybe extreme cross-chaining won't work but otherwise .... it is a matter of fine-tuning via the barrel adjusters .... Not the limit screws.

Your best bet really start from scratch. If the derailleur is mounted a bit crooked or a little too high or low you can have all kinds of issues. I have seen where the front of the cage was perfect but the very back was hitting because of a half-a-degree of twist, and also where the derailleur was a little too high so it would pitch the chain off the outside, but if I dialed the derailleur back in, the back end inside of the cage hit the chain---it was supposed to be below the chain by a few mm but I had the derailleur just high enough that it hit.

Got to the Shimano site recommended above, or go to Park Tools ( )

Seriously, if you can count to three millimeters) you have everything needed to install and adjust a front derailleur. It comes down to precision, which means being careful and patient. Just do it. Once you see how easy it is .... after six tries, if you are thumb-fingered like me---you will be amazed at how simple it is ... and how satisfying.