I never had a problem regarding bottom heat vs tops not browned. We mostly bake with bottom heat ovens! Heat rises, so if you position your oven rack higher it will brown faster. Cakes recommend to be on the middle of the oven (instructions says to place the oven rack in the lower third of the oven but this actually means that when u place ur cake, the cake itself is in the middle or just around there.
The oven needs to preheat for a minimum of 30 minutes. DO NOT rely on the preheat function of your oven. My oven says it is preheated just in 10 minutes but this only means the built in oven thermometer detects the dialed temperature. Most all built in oven thermometers are on the ceiling of the oven! I place my Thermoworks or CDN oven dial thermometer on the rack of the baking cake and it takes 30 minutes!
Again, did u open the oven door prior the recipe baking time? This is the main reason foam cakes such as genoise collapse.
Also, you may want to check if your oven dial thermometer is accurate!
Regarding heating eggs, it won’t cause the collapse. 85-90 oF is fine, I heat mine to 110 actually. Be sure eggs don’t scramble!