@James  noted that SDW(-T) electrodes are just straight rhodium-tungesten rods, without familiar starting aid coils. That means these lamps are expected to be quite hesitant with glow-to-arc, until electrodes and arctube become hot enough.

SDW(-T) lamps actually glow-to-arc somewhat faster when on squarewave electronic gear.

We have a storm of rain: https://www.youtube.com/watch?v=cl1da9rYFeo
And it is 16*C now.

It takes patience, and practice. Prep work also helps significantly.
I was horrible with spray painting (I used to refurbish traffic signals as a side gig), but I learned and got techniques from other collectors. Nowadays I’m more comfortable and do far better work. It’s not a 1 day job, it’s something that could take up to a week.

There’s a vid on YouTube of someone restoring a OV-15, and what that individual did is very similar to how I’d approach your fixture, minus maybe the little details, like filing the craters in the mold.

A subjective option could be leaving it as-is. A good cleaning with Simple Green and water goes a long way. Not to mention you’ll never get that factory Westy paint again, even if it was professionally done.

Yeah but I've tried different hammertone paints already and they don't show the hammertone look nor do I have prior painting experience.

Powder-coating is very expensive, and you’d have to find a vendor who would be willing to do something on the novelty side. Not to mention if you get a scratch or some damage to the fixture (which will happen, wear and tear), it is very difficult to correct.

A more logical and cost-effective option is to use the regular off-the-shelf spray paint. @BT25 has good experience doing this with his Silverliner. It’s easier, less expensive, and easy to correct if there’s imperfections or you get any sort of surface damage to the paint.

Yup, early troffers were listed in catalogues as early as the 1940s, typically looking like modern 1x4 troffers but with deeper housings and glass instead of plastic. In some cases they were open or had louvers.
Rest-Glow
Curtis Lighting
Day-Brite 1941
Day-Brite 1947

At the time, most installations using troffers arranged them in long continuous rows and were 1-2 lamps per cross section although a few 4 lamp models were available. Fluorescent luminaires was still a mix between recessed troffers and surface mounted types such as half pipers and louvered fixtures. Various models were made, including ones for long extinct lamp types such as F90T17. These of course were predominately preheat, rapid start would not be introduced until the 1950s. Most building ceilings at the time were typically wire lath and plaster or 1x1 tiled so in most cases troffers were a lot harder to install compared to surface mounted luminaires.   

Modern T-bar ceilings were only patented in 1958 before then tiled ceilings were typically attached using furring strips with screws, adhered on, or was a removable system where the tiles needed to be removed sequentially. The 2x4 troffers designed to fit into a T bar ceiling probably came out in the late 50s as well. By 1960 troffers resembling modern 2x4 troffers were in catalogues.

Troffers have been around pretty much since the beginning of fluorescent, but I think the most common style seen today came out in the 1960s or 1970s.

As long as I have been alive, these fixtures are mainstream in commercial lighting. The original ones I think have 4 f40t12 lamps and 2 magnetic rapid start ballasts and has a plastic diffuser with one ballast controlling the outer tubes and another controlling the inner tubes. I have seen these fixtures in 1980s movies and TV shows, but how long have they been around?

looking at an official manufacturing chart I happen to have for the fill gas and pressures of T5 tubes, only the 24W and 39W HO types are Half Neon filled, the 54W 49W and 80W are still Pure Argon, and I think most of the T5 HO tubes you have looked at have been 54W ones?

(although of course there could still be manufacture to manufacture variation)

There are two 54W T5 HO lamps at my floor at my hostel. My father have two 24W T5 HO lamps in his room. Supermarkets here, used to have 49W, 54W or 80W T5 HO lamps.

T5 low current emergency lighting types : Argon + small amount of carbon dioxide

That's interestin. What function does the carbon dioxide has in these lamps?