I understand that password strength increases with length ....
The strength increases with the amount of unknown information in the password, which often correlates with the length of the password. But in your proposed scheme you get a long password with only few information inside, at least if the attacker has detected your scheme.
Example: simplify your scheme even more and let the password only consist of different amounts of "A", i.e. "AA", "AAAA" etc. If the attacker knows this scheme then the only information to guess is the length of the password, that is a password with 20 characters will be not really be harder to crack than a password with 10 characters.
You might think that the attacker does not know your secret scheme (i.e. security by obscurity) but in reality password cracking today is no longer done with brute forcing all variations. Instead there are a lot of cracked passwords out there which are used as the basis for password cracking, that is it will try these passwords and modifications of them. Thus unless you have a very original idea chances are high that others had the same idea already and that this idea also got (or will quickly get) integrated into the password crackers.