Some pointers that might be helpful:
1) Relate battles to one another. This could be as low-key as common locations (Capture Hunter's Farm) and common personalities (The Imperial Governor orders you to defend the palace), or as intrusive upon the game as units wiped out in previous games are unavailable in this one.
2) Keep it simple. Minimise book-keeping. A simple way of simulating the strategic elements of the campaign is to offer each player two (or more) choices, and then cross-reference their answers:
e.g.
Player 1 can choose to:
I) advance to the airfield,
II) send out reconnaissance patrols,
III) wait for reinforcements.
Player 2 can choose to:
a) Retreat from the airfield,
b) launch a pre-emptive strike
c) fortify their position.
Then you have a key:
Ia: Play a fallback mission, player 2 is the defender.
IIa: Play a combat patrol mission.
IIIa: Play an ambush mission, as player 2's retreating troops discover and attack player 1's advancing reinforcements(!)
Ib: Play a standard alpha mission. Player 2 is allowed only 1 heavy support as his heavy stuff has been evacuated.
IIb: Play a standard omega mission. All but one troops choice come on from reserves. 8 turns.
IIIb: Play a Raid mission, player 1 is defender.
Ic: Play a Raid mission, player 2 is defender; player 2 gets fortifications/minefields.
IIc: Play a standard nightfight Cleanse, player 2 is defender; player 2 gets fortifications/minefields
IIIc: Play a standard mission: both sides get +200 pts to spend.
As you can see, the more choices; the more complicated it gets... Don't feel you have to be utterly fair ? the decisions made in the strategic phase should affect the battlefield ? but don't weight the games too heavily.
Oh, and if you use this method ? EVERY SINGLE OPTION should conclude in a battle ? otherwise it gets really boring really quickly as people stockpile more and more.
3) Make sure games impact on one another. In this case, we'll take 'Ib' as the result ? if player 1 wins, he captures the airfield...
4) ...Bringing us onto my final point ? clear win/lose scenarios. Have a rule: once three/five/all the critical locations are owned by one player, he/she wins. End of campaign. This ends it on a high ? 'If Dave wins this game and captures the Cathedral, the Orks are victorious!' ? which should encourage players to start another campaign... to get even!