MrsCrab - please don't let me upset or worry you - I understand either way the risks are small. I just don't want any increased risk, which is, perhaps, silly. The way I see it, I am being sold a natural birth as a "birth experience" (FFS - it's not a theme park). We found out I was pregnant 4 years and 5 days after we started trying (and I know this is not long in comparison to many). I had, to an extent, made my peace with never having children, let alone not having a natural birth. I don't give a crap what I "experience" I just want my baby to be OK. And if I can slither off a few tenths of a percentage point of risk by induction/caesarean/walking naked through the town centre screaming obscenities, I will. Completely understand you may feel the same way, or might quite reasonably be a bit saner about it 
I have to confess I had done little research into my consultant's assertion that IVF placentas "wear out" quicker. What I have been told is that, at both hospitals I've been at, they were (initially) adamant that they would not let me go over 40 weeks, but I wasn't told the reason for this - and was a bit mystified - until we moved to the new hospital and the first consultant I saw there explained that for some reason - they don't know why - IVF placentas don't seem to last as long as non-IVF ones, so that there is a greater risk of placental insufficiency at the end of the pregnancy.
The only mention of this that I have been able to find in studies etc (bearing in mind I am not a scientist and have been a complete "google warrior" here) is the following:
www.theguardian.com/society/2014/jan/08/ivf-babies-risk-complications-study
americas.evipnet.wikibvs.org/img_auth.php/e/ef/7.pdf
www.researchgate.net/publication/230879544_Reproductive_Outcomes_After_Assisted_Conception
journals.lww.com/co-obgyn/Abstract/2007/04000/Reproductive_outcomes_after_in_vitro_fertilization.4.aspx
But they appear to be mostly meta analysis of other studies covering a variety of perinatal outcomes. Basically, from reading these I think the potential issue might be that IVF babies are at greater risk of still birth and placental abruption (and there now seems to be evidence to suggest that this is not simply linked to the underlying reasons for infertility). Babies that go beyond term are also already at greater risk of still birth, and I assume it is a combination of these two factors that mean some NHS trusts (and I know it is not all) prefer to induce at term in IVF pregnancies. The fact that IVF pregnancies can also be more precisely dated may also be relevant, but that is me extrapolating from one of the articles below, so could be wrong.
I have then gone on to look at the outcomes for induction at, or slightly before, term. This analysis is very interesting re increased risk of csection following induction:
evidencebasedbirth.com/evidence-on-inducing-labor-for-going-past-your-due-date/
If I've read it correctly (and I may not have done), there doesn't seem to be a statistically significant increase in sections following planned induction, but there is a statistically significant increase in sections following induction after "expectant management" (i.e. monitoring past due date).
The RCOG information also seems to support this:
www.rcog.org.uk/globalassets/documents/guidelines/scientific-impact-papers/sip_8.pdf (in particular see paragraph 2.6)
www.rcog.org.uk/globalassets/documents/guidelines/scientific-impact-papers/sip_34.pdf
The latter may not be relevant to you - I am 36 shortly so while not AMA I'm on the older side - but it contains an interesting paragraph on induction between 37 and 41 weeks, which appears to apply generally and not merely to older mothers (at bottom of page 4 - helpfully no paragraph numbers in this!). It says:
"There is increasing evidence that induction of labour from 37 weeks of gestation also improves perinatal outcomes without increasing rates of caesarean section. This goes against the commonly held belief that induction of labour leads to an increase in caesarean section rates. Studies alluding to the latter have compared elective induction of labour (without medical indication) with spontaneous labour..."
To be frank, quite happy to end up with section if that's the way it goes, though.
The NICE guidelines on induction and section are here:
www.nice.org.uk/guidance/CG70 (they don't specifically mention IVF and, interestingly, don't support my NHS trust's policy of offering membrane sweep at 39 weeks)
www.nice.org.uk/guidance/cg132
I hope this helps and I'm sorry if any of the information upsets anyone. That was not my intention.
Bear, thanks for the support. I think your situation highlights why I feel like such a tool. Basically, you have a recognised reason for needing the intervention that you need. I am in a situation where the advice is different dependent on who you speak to, and unless I get the "right" doctor at each appointment I am going to have to fight. Given that the advice from medical professionals is contradictory, I just want to take the most cautious approach.
Sorry all for the essay. Hope everyone is getting on well. X