Support for the ordination of women, Yes; support for blessings of same sex relationships, No. Support for Nicean canons on bishops, dioceses, etc, Yes; support for the ordination of women, Yes. Support for the ordination of women, Yes; support for lay presidency at the eucharist, No.
Are twinned commitments such as outlined above consistent when held by Anglicans or not? Here I "have a go" at arguing how they might be consistent. My emphasis is on 'consistency', not on proving one or other or all such commitments to be valid. (You may wish to comment on validity but I am unlikely to engage in reply).
I suggest that when Anglicans think through various commitments in faith and practice, especially those that involve some departure or perceived departure from historic norms, a couple of activities are going on. One is a general Christian theological process of reflection and reasoning: is X consistent with universal Christian faith and practice? There may have been more Anglicans than not who have questioned the doctrine of the Trinity, but their questions have been Christian questions, not Anglican questions. The other activity is working out what 'Anglican//Anglicanism//being Anglican' means? A pertinent question being worked through could be, Is Y of the essence of Anglicanism? (A related question would then be, Who defines the essence of Anglicanism?)
In respect of the commitments outlined above, I suggest that lay presidency at the eucharist is an Anglican rather than a Christian issue. The New Testament gives no indication who presided at the eucharist, so Christians looking to the New Testament for guidance about such a matter are not prohibited from pursuing it. But Anglican Christians have a constraint: it is (so I and many Anglicans would argue) of the essence of Anglicanism that we are a church ordered in such a way that only bishops and priests preside at the eucharist. By constrast it is not of the essence of Anglicanism that only men may be ordained. Providing satisfactory Christian arguments support the case for the ordination of women, an Anglican Christian may consistently hold to the ordination of women and to the prohibition of lay presidency.
The Nicean canons relating to bishops and dioceses are a little trickier. In re-forming the Church of England in the sixteenth century nothing was said in the BCP or the 39 Articles about directly sticking to those canons, come what may in changes to ecclesial life. It could be argued that they have no ongoing application to Anglicans. However in retaining bishops, it could be argued that the Church of England implicitly retained a commitment to the general historic structure of episcopal leadership, thus an Anglican could hold to the Nicean canons as well as to the ordination of women to the episcopate.
How about being committed to the ordination of women and not to the blessings of same sex relationships (or to variations such as committed to both or committed to the latter and not to the former)? I do not see that it is of the essence of Anglicanism that men only are ordained or that only heterosexual couples have their relationships blessed. These questions are 'Christian' questions about how Christians read Scripture, understand tradition, and engage reason in theological reflection. (The exception would be where Anglicans are hesitant to agree to anything in these areas unless the Roman Catholics and Eastern Orthodox also agree to them: that hesitancy is likely to be peculiar to Anglicans and not shared by Protestants). Can Christians (and thus Anglican Christians) hold to consistent positions on these matters? For some the matter will turn on the general basis for consistency. Scripture, for example, is argued to be supportive of ordaining women and not supportive of blessing same sex relationships. Justice demands, others would argue, the inclusion of women and gays in all aspects of the churches' ministries, so we ordain women (and gays) and bless same sex relationships. Yet others could argue that the tradition of the church is crystal clear re ordination only for men, but ambiguous about blessing relationships.
Well much much more would need to be said to satisfy all comers on debate on these matters. My point here is simple and twofold: I suggest 'consistency' in Anglican theologies is relatively easy to achieve in a number of instances relating to contemporary debates, but it is not achievable in all instances. Where consistency is not achievable (e.g. re lay presidency and associated commitments) the intriguing question is raised, who decides what is of the essence of Anglicanism? Which brings me back to the case for the Covenant ...