I agree with your evaluation of the Linc market and the fact that you stand the best chance of using newly acquired skills if you leverage your industry-specific knowledge.
However, as you have rightly identified, you will encounter the common problem of having no commercial experience of whichever skill you learn, though both Oracle and SAP are in greater demand than many other skills. A number of organisations across the UK are recruiting for SAP projects, but they are unlikely to hire anyone without a good knowledge and experience of SAP. This may change as demand grows.
I believe Oracle offers a larger number of roles, and the training is generally more accessible and affordable. SAP training is relatively expensive (up to £6,000 for certification in the BW module). One option would be to do the training in South Africa or Australia, where it is significantly cheaper.
One final idea: do any of the organisations that you have worked at in recent years use Oracle or SAP? If so, you could offer yourself (post-training) at a discounted rate for six months to give you the essential commercial experience.
Solution by Michael Bennett, Best International
The panel: MSB International, Best International, BCS, Computer Futures, Computer People, Elan, Reed Computing, Netheads Consulting, Zarak Technology, E-Skills UK