The 400H is just the higher precision version of the HP 400 family, which had a VERY long history with HP, probably over 30 years, so there are lots of versions, usually differentiated by changes in the serial prefix. (The earliest models did not have a prefix.)
The very first thing to do with any member of this family is to replace all 4 of the large cylindrical capacitors. If yours are still the originals, they will be leaky by now. One of them is in the PS and minor leakage won't be a problem, but you might as well replace all of them while you're at it.
The other 3 are interstage plate to grid coupling capacitors. Leakage here will raise the grid voltage of the following stage, pushing that stage toward saturation, poor performance, lots of heat dissipation, and reduced tube life. Good quality Mylar caps make better than original replacements. Each of these three also has a mica cap in parallel with it, and sometimes I've found one of those to also be leaky. Check each grid voltage to see if it agrees with the schematic.
Once you get these fixed, you can move on to the problem you asked about. I don't have any specific recommendations for that problem, but I'd suspect a problem with poor contact in the range switch. Treatment with Deoxit followed by Shield should be good for this.
If you continue to have problems, post your serial numbers/prefixes so we know what version you're working with. I probably have 5 different manuals for the HP400 series, and I'm sure I'm still not completely covered.
