My basic goal is to look up a Greek word and be able to find cognates in other languages that will help me to memorize its meaning. A technique that often works is to look up the Greek word on English wiktionary, and if the etymology points back to a PIE root that has a wiktionary entry, click through to that and look at words in other languages derived from that. However, sometimes the wiktionary entry lacks an etymology. In this case I can look up the Greek word in the etymological dictionary by Beekes (Etymological Dictionary of Greek), then if there is a known PIE root, look up that root somewhere else (e.g., I have an American Heritage dictionary from the 70's that has a short PIE dictionary as an appendix).
The problem I'm having is that when I try to correlate these different sources of information, I find that they're using different conventions and reconstructions. So for example, Beekes tells me that ἔλδωρ (a wish) is from h1ueld. Only with a bit of luck was I able to stumble across the PIE root gheldh here and find that they interpret it to mean "to desire, wish for," which makes me think it's the same root -- although many sources call it "to pay," which would not have clued me in.
Is there a finite number of conventions or reconstruction systems for PIE roots, or some effective way of translating (at least with decent probability) from one system to another? Googling has led me on interesting excursions into the laryngeal hypothesis and such, without getting me any closer to finding a workflow for my task. Does wiktionary's system have a name? Does Beekes's?