Hi Pavel88 and welcome to the forum.
As you have figured out, and as I can confirm, the Badawi/Hinds dictionary (which is EA to English) is not available in an English to EA edition.
Unfortunately, I don't believe there is a comprehensive English to EA dictionary.
What I do in this situation is look through an English to MSA dictionary to find a word and then look up the MSA word I found there in the Badawi Hinds to see if it occurs in EA. Often this works, but of course it may not work in all cases as the EA equivalent to an MSA word may be different.
Other than that, the only suggestion I have is to ask here on the forum. This may be better than looking in dictionaries anyway, as they (dictionaries) can be prone to errors, or don't always show how a word is actually used in real context.
And yes, Spiro's dictionary is outdated and not recommended. But since you have it, you could always see what word Spiro lists and then see if it is listed in the Badawi/Hinds.
Sorry I could not be of more help.