You're going to have to provide some form of support and lock down for your lens, as it's moving up and down on the lens mount. I have my lens supported on a Y support attached to an Arca Swiss plate, but 15mm rails will do the same, and then the lens is tied down with zip ties through the holes on the Y support.
This works fine for me, as I never change the zoom lenses on my two cameras, so zip tying doesn't matter. That said, it' easy enough to remove the zip ties and then replace them. You can get reusable zip ties as well or thin Velcro straps.
EVERYONE else has this combo. It the most popular combination.
Get longer rods in front and add a small rig lens support: SMALLRIG 15mm Long Lens Support Bracket Height Adjustable for DSLR Camera Shoulder Rig (New) - 1087 https://www.amazon.com/dp/B00E3OATAK/ref=cm_sw_r_cp_api_i_5XWH5CBWYH0THSJEJG9Q?_encoding=UTF8&psc=1
Yes, that's an incorrect screw as you can't screw into two threads and get the plate in tight (unless you're very lucky). That screw set should give you everything that you need.
The base plates are called Arca Swiss, it's a generic name for these camera plates, much like NATO rails. They come in numerous different lengths, much greater options than with Manfrotto 501, and they all machined alloy (Manfrotto plates are often cast) alloy.
I can't find where I bought the lens support, but if you look at this image, the support I use is like that screwed into the SmallRig rail mount: https://www.amazon.com.au/SmallRig-Support-Bracket-Adjustable-Shoulder/dp/B00E3OATAK/ref=sr_1_1?dchild=1&keywords=lens+support&qid=1615936292&sr=8-1. I was able to buy two of these just on their own for way less. I just screwed the support into the Arca Swiss plate at the right point, adjusting the height with washers.
My supports also had 1/4" threads, so I could screw them in from underneath with an appropriate screw. If the one depicted doesn't, then a suitable screw will need to be placed from the top. The slots are also useful for attaching zip ties to further secure the lens.