generally, yes the above are reservation only and yes, lack of japanese may be difficult for walking-in. however, if you can successfully reserve online without a Japanese phone number, then you should be fine.
I see wide open availability for the rest of the month right now for both Beppu Hirokado or Tanakada.
often, restaurants that want Japanese speakers only will say so in their reservation policy before they treat non-Japanese as a no-show. we got along fine at Tanakada and I believe they had an English menu, though we knew what wanted already. i haven’t been to Beppu Hirokado but I’ve been to Ginza Shinohara from where the chef came, and they had good service.
of course there are many, many other places to try but it’s generally better to make reservations. on the first night of my last trip to Tokyo, I tried to walk in to 5 places (2 of which were casual pizza) and they were all too busy. perhaps Fukuoka is different. but if you want walk-in, then maybe some izakaya and a backup noodle or curry joint nearby is a plan.
Motsunabe is a popular local offal hotpot meal. I’m partial to the miso broth. Yamanaka is a good fancier chain, however you can find motsunabe practically everywhere in the city.
Also if you’re into chicken skin. Torikawa is a local crispy grilled style. There are some specialty places however many izakayas and most yakitori joints have it on the menu. I’m partial to shio - crispier.
ah yes motsunabe, great stick-to-your-ribs dish for fall/winter. maybe tough for 1 but excellent for 2 people. at home, i like it with shochu (Satsuma Ohara) and soda or a crisp sake like Morishima’s omachi junmai daiginjo (great peppery finish would work well with a robust motsunabe in particular) or one by Yamagate Masamune.
