There are two ways you can do the 点前:

• Facing the 瓶掛. In that case, 建水 goes directly where it's going to live and doesn't move during the 点前 (🅰️)
• Slightly facing the guest. In that case, come in with 建水, face the tray, shift the tray (and yourself), then move the 建水 to the 炉 position. In that case, 建水 moves before you clean the 茶杓 (🅱️)

• It's also quite possible to do it with a 釜, bringing in 柄杓 and 蓋置 with the 建水. Quite a few teacher use this uncanonical form to get students used to the 釜 without introducing all the additional woes 運び brings.
• In 炉, however, things get a bit muddy, so this is my conjecture:
  • 🅰️ If you want to stay in 略盆 country:
    • come in with the tray facing NE, and then id. with the 建水, putting it where it needs to be.
    • Like this 建水 doesn't move, nor does the 盆. In that case, there's still the question of when to unload the 建水.
      • I'd unload the 建水 before the 点前. This feels a bit tidier to me.
      • but you could also unload it as needed (when you'd close the lid in normal 略盆).
    • Since there's no 拝見, I'd argue that you 棗・ポンポン, then close the lid, keep the 柄杓, take the 蓋置 and 建水 (shifting a bit, if you're so inclined), and get up to leave. This get's slightly awkward if you have a 蓋置 that needs turning.
  • 🅱️ You could do it like in 棚:
    • The tray is placed N, then with the 建水 you sit down facing N, too. Then you move the tray (and yourself) to NE.
    • In normal 略盆, now you'd move the 建水, but with the 釜, it is loaded. So unpack it now, then move it.
    • When finishing, you'd first put the 柄杓 on the 建水, then move the tray to N, then leave.
• It's also quite possible with a 鉄瓶 in the 炉. In that case, I think the spout shout face the 盆. In order to not show the back to the guest, pick it up with R, give to L, take 帛紗 with R when using it.

Of course, absolutely not part of this 点前, and if you feel you might end up in a situation where the guests might want to 拝見, why not do 千歳盆 to begin with…? In saying that, drawing inspiration from 千歳盆 (and 御所籠 and 卯の花):

• After placing the 茶筅 into the 茶碗 (but before moving the 茶杓), take out a 古帛紗 and transfer 茶碗 there.
  • In 千歳盆, you'll clean the 茶杓 now and put it on the 茶碗. (Then 棗 to the middle, close the 鉄瓶's lid.) Since you want to present the items on the 盆, but the 薄器 is where the 茶杓 needs to go, I think the 千歳盆 approach is a good solution.
  • Clean 茶杓, put it on the 茶碗, move 棗. Take the tray to the guests, purify the 棗, put to the R, add 茶杓 and give them.
• You might also use a 古帛紗 akin to the 色紙 for the 薄器 and the 茶杓. In that case, you wouldn't need to put the 茶杓 on the 茶碗 first, but do it like in 卯の花 (棗・茶杓, sort, 茶碗 to the middle and tray to the wall. After 拝見: 茶杓, 茶碗, 棗.