What you're trying to do is a very big leap. Realistically you might need to find an extra stepping stone or two between private client and in-house - eg private client to mixed tax to corporate tax to in-house.
Or a general practice role that would enable you to pick up indirect tax or corporate tax experience. But you need a stepping stone because you're currently specialised in the wrong tax for what you want to do and you wouldn't be an "experienced" hire in a different tax.
Private client straight into in-house corporate tax or indirect tax with potentially tax provisioning, quarterly instalments, setting up CT processes, giving advice on M&A, transfer pricing, SAO, country by country reporting, pillar 2... Easy to see why employers are not persuaded. The risk to the business of taking on someone with responsibility for those complex areas when they have no prior experience is far too high.
Have you had any exposure to any of that kind of work? Done any training or CPD in those areas? If not I think you need a plan to develop those expertise first and find some smaller stepping stones like pp's example of their transition from tech support to marketing.
Would you be able to pass a corporate tax technical test at interview? If so, great. If not, how would you propose to do the role anyway (especially considering PCRT)?
Which exams did you take for your CTA? You could consider doing an ADIT paper on a standalone basis to develop and demonstrate your larger corporate knowledge (eg the UK paper).