Be aware that a UK-based company typically doesn't add very much value for many long-haul destinations. They take your requirements to an incoming travel agency, which gives them a price. Then they add 30% and then VAT is slapped on top, whereas if you pay a Japanese agency there is no UK VAT - and any Japanese sales taxes can't be offset against VAT, as used to be the case with European VAT pre-Brexit. (The incoming travel agency also subcontracts the transport and guiding to local offices in each town, but it's harder to get their addresses.)
There is a list of Japan-based incoming agencies here: https://www.japanlivingguide.com/lifestyle/travel-attractions/travel-agencies/
I mention all this for two reasons.
First, we went on a tour of Korea and Japan in 2023, via an American agency, and while it was very good, when we were there and looked at the rack rates for the hotels and services that we were getting, we realised that we were paying a hefty margin to the agency for not a lot of work (we had to book our own flight from Seoul to Osaka, for example). And we didn't even pay VAT because it was an American company.
Second, we have just been on a tour of India which was put together for us by an incoming company and it has been incredibly good value for money; all that a UK-based agency would have added, as far as we can tell, is a layer of extra communications, plus their margin and VAT. We are paying just over half what a family member paid for a (UK-coordinated) tour of comparable duration and quality. The local agency's logistics have been impeccable, including booking our internal flights. And all we had to do was send a few e-mails (plus a little bit of due diligence to reassure ourselves that the agency was a real company - it is a little scary sending a bank transfer of £4,000 to India!).
Anyway, this was just an idea for how to maybe make your budget go further. If time and resources permit, you could also consider spending 2 or 3 days in Taiwan, which is very interesting (and might not be around as an independent place for much longer, if Trump and Xi have their way). We found Korea, and especially Seoul, a bit fake in places, lots of people very concerned with appearances... but maybe that's a bit unfair. And Japan was completely fabulous, we'd love to go back.