A Review of the Greek
More or less, this is a so-called 'literal' translation. Exept that it isn't even English in certain places (e.g. "thy will of yours").
On the site itself, it cites the Greek word corresponding to its translation in the text.
Here is the Greek for the prayer from Matthew 6,1 followed by how I would 'literally' translate them. I've bolded the words and their corresponding translation so you can see what is translating what. (The brackets denote helps for understanding the text, and are not translations of the text).
Πάτερ ἡμῶν ὁ ἐν τοῖς οὐρανοῖς·
Father of us who [is] in heaven,
ἁγιασθήτω τὸ ὄνομά σου·
Treated-as-holy [may] the name of you [be].
ἐλθέτω ἡ βασιλεία σου·
Let-come the kingdom of you
γενηθήτω τὸ θέλημά σου,
Let-be-brought-about the will of you:
ὡς ἐν οὐρανῷ καὶ ἐπὶ γῆς·
As [it is] in heaven [so] also [let it be] on earth.
τὸν ἄρτον ἡμῶν τὸν ἐπιούσιον δὸς ἡμῖν σήμερον·
the bread of us for-[our]-sustenance give to us this day.
καὶ ἄφες ἡμῖν τὰ ὀφειλήματα ἡμῶν,
and forgive us the debts of us
ὡς καὶ ἡμεῖς ἀφήκαμεν τοῖς ὀφειλέταις ἡμῶν·
as also we forgive the debt-owers of us
καὶ μὴ εἰσενέγκῃς ἡμᾶς εἰς πειρασμόν,
And [do] not lead us into temptation
ἀλλὰ ῥῦσαι ἡμᾶς ἀπὸ τοῦ πονηροῦ.
But deliver us from [all] evil.
As you can see, the way of denoting the possessive (e.g. our trespasses) in Greek is to say 'the trespasses of us.' Which is translated, of course, 'our trespasses' as it should be in actual translations. Let this account for the awkwardness of some 'literal' translations which retain the word order as I have done (they aren't translations at all, since they only usually obscure the language, and don't translate it properly speaking).
'Debts' is an Aramaism for trespasses and wrongdoings against one's neighbour (sins), and is not a monetary debt in this context (this is why Luke has ἁμαρτίας—'sins' instead of—there can be no doubt—Jesus' original ὀφειλήματα—'debts').
Is "draw us to you" a valid translation of the Greek sources?
This is an attempt, according to the website itself, to translate ῥῦσαι, which means to 'deliver' or 'rescue' from something (the state of bondage or danger from which one needs delivered), implicitly, therefore, into something else (i.e. not that state).
They argue that the implicit object, implied in the verb, into which we are delivered is 'you' (God), but this isn't justified from the text. To deliver from evil or calamity, ill-fortune, wickedness etc, is not to say we are being delivered 'to God' but simply out of those things. To say 'God' is to presume too much.
This alone disqualifies it as a 'literal' translation so-called. Because it takes interpretative liberties usually reserved for more 'dynamic' translations, i.e. that used in most Bibles—this being a particularly 'dynamic' translation at that.
'That which is grevious' I would exchange for something which connotes the same thing most common translations do, as well as the word itself in Greek (πονηροῦ). 'all ills,' 'evil,' 'the bad,' 'all afflictions.' All that is an affront to peace with God (since it parallels πειρασμόν in the passage—tempation, trial, calamity). (the Latin Vulgate simply has malo—'evil,' as most translations do).
They have translated 'free' for ἄφες instead of 'forgive' where the context is clearly sins, and the New Testament uses ἀφίημι (the root verb) to be 'forgive' (i.e. forgive sins) all the time for example:
Ephesians 1:7 (ESV)
In him we have redemption through his blood, the forgiveness [τὴν ἄφεσιν] of our trespasses, according to the riches of his grace,
Obviously, God doesn't pay our debts for us: forgiveness of sins is meant here. The 'cancellation' of debts here obviously means 'forgiveness of sins'.
I hope this clears up something for you. If not, let me know.
1 Nestle-Aland Novum Testamentum Graece 28th Edition. Matthew 6:9-13.