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Could she or I apply for visitor visa again in a couple of months for her to come and stay for approximately 5 months (if the spouse visa is not viable)?
There is no required cooling-off period between visits, and Americans generally do not require entry clearances. But stays like that start to get dicey. First we'll look at the guidance (sorry for the page break)...
...this echos what is written in the rules, Appendix V 4.2 (b)
(b) will not live in the UK for extended periods through frequent or successive visits, or make the UK their main home; and
...and if your wife has just left from a 4 month visit and then wants to return for a 5 month visit, the Immigration Officer will be entitled to assume that she is making the UK her home. So she should expect a challenge, the outcome of which will depend upon her personal impact and articulation skills. If successful, she will get 'stamped in' for 6 months; if not successful, she will either get a temporary admission (not a good thing) or she'll be served removal papers (a bad thing).
Many times Americans in her situation will get an entry clearance beforehand (even though it's not required) because it avoids wasted air fares and the distress of removal from port.
Or will I have to wait a certain amount of time, since she has been here for 4 months (and 1 month before)?
Wrong. It's her landing interview and her her responsibility to either apply for entry clearance or to explain herself to the IO. You are a sponsor and a stakeholder, and getting the roles mixed up can set off their radar.
In summary, the answer to your question is indeterminate. In theory and on paper what she proposes to do is fine. But the IO has the option to see things differently.