Many thanks, everyone, for your fast responses. I think I'll hold on with the switching. The 55-300 might be actually worth keeping. I do have lots of keepers which were shot at 300 mm, even close to wide-open. The speedy AF is a great thing and I'm afraid I'd regret not having it. I might take the lens for another Single-In challenge to explore it more.
I have also considered other options (F/FA 300 - but they are rare where I live and even more bulky than the DA). The DA 1.4 converter would be a natural continuation but I need to stay reasonable when it comes to expenses
and I couldn't afford to buy both (the lens and the converter). So if I was to sell the 55-300 to cover less than half of the price of the second-hand DA300 I'd have to be sure to gain enough - and now I'm not.
OTOH, it does sound very reasonable to buy the DA 300 at some point and to decide later if I need to keep both.
Thanks again for your valuable input.
EDIT:
Ok, now I can see that the FA 300 is actually lighter than the DA 300 (surprise as the former one is a FF lens). Still, they are much less abundant here where I live so probably that's why I wasn't thinking of it.