When I looked for live in carers (dad was terminally ill cancer, mum then moderate vascular dementia) it was continuity of carers that was most important. My parents needed a carer experienced in both dementia and palliative care.
I began my search late one Saturday pm. It was interesting to see how the different companies responded to an out of hours enquiry, as a possible indicator of the response that I might have had in any future emergency. One company, whilst unable to provide live in carers themselves, were a mine of information and gave me the name of a company that they had worked with in the past, The Good Care Group.
I had quotes from two companies in the end, both £1000+ per week (Home Counties) but offering very different services. We went with the "same two carers alternating every two weeks" as opposed to "a carer from a pool of five, alternating weekly".
Having over the last nine months discussed it with the live in carers, the problems of "get out of my house" and resentment seem more of a problem where it is the female resident suffering from dementia. Certainly for my mum, who had not worked once she married, her home and it's efficient running were entirely her domain, having live in care was very problematic. In fact we always refered to the carer as a "nurse" and told mum that she was there to look after dad, otherwise he would have to stay in hospital.
Despite mums best endeavours TGCG were with her for 9 months. All of the carers during that time were knowledgeable, caring, thoughtful and hugely supportive to us the family. Two are still in touch by text and email with me. The company itself were fantastic; they sent their dementia specialist to assess mum when we had concerns about her behaviour, and I could and did call them at any time, knowing that they would respond. The live in carer practically supported mums recent move into the care home; preparing her clothes, visiting it with me and mum in the preamble, and afterwards when mum was a resident. The live in carer was able to help me with the endless form filling about what mum was like, triggers, positive effect phrases, subjects to avoid, etc.
At the time live in care was exactly what my parents needed, now with my father having passed away and mums dementia more advanced, she is without doubt better suited to being in the care home.
Cost wise the live in was a little more expensive, and provision of daily two hourly breaks also needs to be factored in.
Good luck with your search.