If I understand you correctly, you want to tilt the unit DOWN in a climb, so that it looks along your vertical track, rather than along your heading. That is, where you are going, rather than where you are pointed.
So you would tilt it down by the same amount that your angle of attack has increased over your normal cruise attitude.
If this is correct, then Sick Squid's 1st law, if you rewrite it as Angle = fpm/(2 * knots) is a rule of thumb for Angle of Attack. So this gives (at 200kt) 1000 fpm 2.5 degrees; 2000 fpm 5 degrees; 3000 fpm 7.5 degrees. Does that sound close ?
Sick Squid's 2nd Law for looking forward and down umpteen thousand feet is a very good one, except for almost underneath you. 10,000 feet down, 25nm ahead, Sick Squid says 4 degrees down. Trigonometry says 3.76. Same level of accuracy holds in range 2,000 to 30,000; 15 to 50nm
ET