As I strongly, strongly recommend to play Space Hulk with the original first edition rules (I would like to see a Old School Renaissance for Space Hulk too) here are some rules which miraculously presented to myself while I was analyzing the original rules. Behold the ‚Basic Psychic Rules‘ for Space Hulk 1st Edition.
The following houserules are are a fully compatible subset of the Genestealer extension psychic rules and are easily extendable to the original Genestealer rules. They are mainly a modified presentation of the original Genestealer psychic rules. There are no additions to the Genestealer rules. The part mostly changed besides the different presentation is an adaptation of the card system into a dice roll (and thus the renaming of ‚psychic cards‘ to ‚psychic powers‘), which still fully preserves the probabilities of the Genestealer psychic rules. They are in short the whole psychic rules from the Genestealer extension except of psychic attack cards and the associated rules of psychic effect marker decay and dispersing, psychic level mastery, targeting, dispelling and enhancing psychic attacks (force battles). They consist of the remaining ‚basic‘ psychic rules: managing the hand of psychic cards, enhancing close assault rolls and playing Aura cards. Thus they mainly allow psychic rules which are mimicking the rules as in the Deathwing extension and allow a hard-to-hit-rule like the Patriarch/Broodlord has in the 3rd and 4th edition of Space Hulk (don’t forget that the Patriarch rolls 4d+3 in close combat in the 1E rules).
All you need to play with these rules is some additional cups to covertly roll for psychic powers and some differently colored dice. They are completely usable with the components from 3rd and 4th edition of Space Hulk. Have fun.
The aforementioned Genestealer extension to Space Hulk 1E.