First off sorry for being a bit argumentative and questioning your knowledge of the issue as it doesn't help the discussion at all.
As far as I know the 24/7 access will be to all sites that Iran has declared...undeclared, suspicious sites and military installations are not included. Under the deal Iran has the ability to dispute these sites through an appeals process that could take up to 24 days (including 3 days to implement the appeal board's decision)...and if Iran doesn't comply after 3 days there is another dispute resolution clause that allows up to 50 days of evaluation. Suffice it to say there would be ample time for Iran to hide any activity at these sites in advance of inspectors.
Another big issue I have with the deal is the inclusion of the removal of UN weapons embargoes imposed on Iran for weapons import/export and ballistic missiles. Apparently China and Russia pushed for this under the guise of allowing Iran to more effectively combat ISIS. Just last week Secretary of Defense Carter and the Chairman of the Joint Chiefs of Staff testified that under no circumstances should these embargoes be removed. Why include these in a deal aimed at curbing the nuclear weapons program?
As far as the alternative that I would have preferred, I would have preferred continued sanctions and, if necessary,more sanctions to attempt to pressure Iran to accept a better deal and allow the US to negotiate from a position of strength. A better deal would not have included lifting of weapons embargoes, would have provided more oversight and comprehensive inspections, and gone further to push back Iran's timetable to achieve a nuclear weapon after 10 years.
We have ingrained in the agreement, per the presidents mouth, access to any suspected sites. And we have 24/7 access to their entire nuclear infrastructure. How much more comprehensive can you get? This is after all an autonomous nation. With international rights that we have sworn to respect in the UN. It isn't realistic to expect occupational authority like they are our subjects. From what I have read all seems very reasonable and skewed heavily in our favor.
The problem with your logic is that Iran can't magically produce everything they need at one small underground site like this is some 70's Bond movie and they have an underground layer. By having access to all of their supply chains and current facilities they would literally have to create a vast underground network that operates completely independently from their already established infrastructure. Otherwise we are going to catch wind of it. Needless to say that would be insanely difficult, expensive and time consuming to achieve on Iran's part. They would in fact just be better off breaking off the agreement and repurposing their current infrastructure if they were so hell bent IMO. Not to mention the logic doesnt add up. If they are so determined to go that route then why make those initial offerings years ago? Why not just batten down the hatches and get the final push and get that nuke? Why? Because they know that while they will have a bit of leverage in some ways if they get one, they will be deeply affected economically for the foreseeable future. Long term diminishing their power as a nation domestically and abroad. So they are seeking this deal primarily because of economic interests. Long-term I'm sure they still have an interest in getting a nuke but this deal effectively eliminates that possibility for at least a decade. As opposed to nothing which likely guarantees them obtaining one shortly.
As for the weapons embargo, well, its not ideal but at the same time Iran has the right as does any nation to sell weapons. And as I said earlier the terrorist related sanctions remain in place. So it isn't like it is going to be a cakewalk for them to sell them. And frankly they have done just fine going about their interests in that regard for the most part. This is hardly a deal breaker.
As for your alternative. It sounds good in theory(just continue to sanction them until they bend even more!!) but reality is another story. The alliance we have forged right now is hinged on getting Iran to the negotiating table to curb and control their nuclear program. It is established with rather unwilling bedfellows like Russia and China through the UN. Without their support much of the teeth of the sanctions begin to unravel. Giving Iran more breathing room. Hurting our leverage to obtain any goals we seek, let alone the more challenging ones you seek. To which they would become even less plausible to achieve.
As you said China and Russia fought against the weapons embargo, so why in gods name would they suddenly be on board with tougher sanctions if we all of the sudden told them that we will walk away from a deal if they don't bend on this side issue that was not what the initial alliance was formed about?