If you've overexposed, you want to pull rather than push your film.

Film pushing involves developing to higher than normal contrast, which causes a given exposure to produce more density. Since this is proportional to exposure, exposures barely recordable move up to low-mid tones, middle exposures move up to high-mid, and highlight level exposures "block up" -- becoming too dense to print by the old optical, silver-gelatin methods.

In your case, with film that has received a bunch of extra light, you need to do the opposite. By developing less than usual, you'll keep your overexposed highlights from blocking up, and preserve your ability to print or scan negatives that would otherwise be too dense.

In fact, what you did (exposing by two extra EV over what should have been correct) is often done intentionally by photographers, in order to obtain good shadow detail, with reduced development then applied to tame the highlights.

Fortunately, there are published developing times for HP5+ at EI ranging from 100 (which is about what you actually gave) up to 1600 or more. Just look up the correct time for your chosen developer for HP5+ at EI 100, and develop that way -- you may find you like the result enough to do it intentionally on a regular basis.