In ROCOR vulgate and septuagint translations are heavily promoted and are more normative.
There are several priests in the AWRV who would prefer to use the douay rheims for readings at mass.
One of the problems (depending how you see it) within the Antiochian WRV, is that those with the power over liturgy are against the use of the Vulgate for english language liturgy, for latin it is the only option, thus in that manner it is allowed. Even though I think it is a mistaken practice to continue to base english texts entirely on the masoretic and KJV, I understand their reasons. I believe that the reason for it is more practical than dogmatic.
One of the special reasons that the Antiochian WRV has been able to have success is because it relies for the most part on existing Book of Common Prayer inspired liturgical texts used by Anglo-Catholics formerly in the Anglican Church. It takes a number of expert translators and editors to correct these translations and bring them into a pure vulgate or septuagint translation.
I believe that the view can be described as "if it ain't broke don't fix it". The anglican liturgical patrimony has been proven to be for example far more stable , reliable and satisfying than the contemporary english translations by the Roman Catholic Church in the last decades (Although their pre-1966 translations were much better), not to say their 2011 translation is not an improvement, but it did take 40 years to get to it.
I believe that there is a concern that any change in liturgical text is going to bring about unnecessary complications and make people uncomfortable. For those who have attachment as former protestants or anglicans to the text of the Book of Common Prayer, King James Bible or Coverdale Psalter, they may have a feeling that "their old friend" is leaving them. They are used to saying the same words for their whole life, any change in this, even for good reason brings about a certain suspicion that many feel is not worth bringing.
ROCOR has it's own issues. Under the former Fr. Anthony Bondis direction (he is has now left the church) there was heavy promotion of contemporary english and the RSV 2nd Catholic Edition bible for readings at mass and the office mostly within an altered tridentine rite mass. Supposedly over time, last we heard, the traditional 16th c. english is required to become normative in the ROCOR western rite and their contemporary liturgical texts will be replaced with that, bringing it in line closer to the Antiochians translations. Whether this is still going to happen, I do not know, but that was the word from the four man commision around August of 2013.
ROCOR, being smaller, less established, and less interested in being tied to a pure anglican liturgical patrimony is definitely open to corrections in the name of Orthodoxy, as it has less to lose and supposedly less of it's lay people will mind. In ROCOR the book "A Psalter for Prayer" by David James is the same Coverdale psalter used in the Antiochians WRV except that it has corrections from the vulgate and septuagint. Many parts of it are identical to the original Coverdale, but particular words, and in some rare cases, a few entire psalms are noticeably different. Judging by its reviews on amazon.com it is a great success as far as balancing familiar text with beauty and accurate translation. http://www.amazon.com/Psalter-Prayer-Adaptation-Translation-Instructional/dp/0884651886/ref=sr_1_1?ie=UTF8&qid=1395435404&sr=8-1&keywords=a+psalter+for+prayer
Currently most people who use "A Psalter for Prayer", use it only for the byzantine rite. For that reason I have been creating a pointed psalter based on it, to use in the latin rite divine office. It should be appreciated when it is ready. If the Antiochians would adopt the "Psalter for Prayer" text as their official psalter, it would go a long way toward improving the situation. However it would certainly bother some who already own the original uncorrected coverdale in the form of a breviary or st. dunstans plainsong psalter.
One can understand why this may not happen and could be challenging to introduce, yet it still seems necessary to eventually do so.
My own view is that the liturgical patrimony of the anglican "catholics" from the anglican protestant church is basically good, but that it does EVENTUALLY need correction. That correction ought to be minimal and as little as possible however.
In the average Sunday Mass for the Antiochians, the majority of texts are alright. The problems with translation begin moreso when you are singing all 150 psalms and using the entire King James Bible for reading large passages of scripture (Matins lessons for example.)
Therefore the biggest problem with relying on a flawed translation in my opinion comes not in the Mass, but in the Divine Office.
However, since most people do not focus on the divine office, this is not much of a concern.
I think this sums up the matter succintly.