(a) Raise difficulty setting. (You can do this mid-campaign but it won't have as much effect as if you had done it at the start, because your army will be stronger than if the previous battles had been harder fought).
and/or
(b) Set campaign as Progressive difficulty. (Only possible on starting fresh campaign)
Note that the campaign difficulty setting defaults to effectively half a difficulty setting lower than the equivalent single battle difficulty setting. If you set the difficulty as Static, it remains like this for the whole campaign. If you set it as Progressive it starts like that, but gradually scales up until it is half a difficulty setting above the equivalent single battle difficulty setting for the last battle.
If your battle losses are less than (approximately) 15%, subsequent battles will be somewhat easier. If your battle losses are more than 15%, subsequent battles will be somewhat harder.
However, overall, if you usually play single battles on difficulty 3 and get a good tough fight, then you should set the campaign either to level 3 Progressive or level 4 Static. Rinse and repeat for subsequent campaigns until you find the settings that suit you best.
(b) Use Paul's TT mod?
Would have no effect on difficulty as it does not alter gameplay in any way. Also it can only be used for Sandbox campaigns.
(c) Use the global AI mod?
Would make the battles slightly more difficult - probably not as much as increasing the difficulty setting.
(d) House rules?
Should not be necessary until you get to the point where you find Deity level Progressive too easy.
(e) Wait for 1.5.20 to come out of beta?
Would not make any significant difference to this particular campaign as the AI improvements only apply to cavalry armies.
