"The offer will be subject to inspection, so I could keep the offer high, and then dicker after the inspection, when both parties are more "bound".

Not necessarily. You are tying up your time with a house that you think has a serious flaw ... hoping to get the seller to negotiate and/or repair before closing.

"It really needs to be evaluated by a structural engineer. How do I push that?"

Walk away ... from what you have said, it's probably a serious structural flaw that will require excavating and dealing with the expansive spoil or bad drainage.

Or, put in the contract that the offer is subject to the foundation inspection by the structural engineer of your choice, at your expense, with repairs to be done by the owner before closing.
(or lower the offer it by the highest estimated cost of repair and offer to pay for repairs yourself)

If this is really the house you want and are willing to deal with the worst repercussions associated with the crack, then lazygardens is correct about putting the engineering inspection in the contract.

The home inspection clause is for NEW problems that are discovered, not for problems that are easily visible to a buyer during a walk-through. It's like the difference between a heavily worn or soiled carpet (visible) and a broken water heater (found by home inspector). If you make an offer knowing that there is a big crack in the basement, then you are accepting it at that price.

Horizontal cracks like the one you describe are definitely a sign of bowing walls. This problem can be caused by a combination of poor foundation drainage and soil composition. Clay soils are known to cause this problem because they expand when wet and shrink when dry.

The good news is that there are technologies out there that can improve drainage without having to dig out the foundation and install new french drains. There are also many options to stabilize bowing walls or return them to their original position, ranging from wall anchors, helical anchors, I-Beams, wall braces, carbon-reinforced strips, etc... all of which are less disruptive and more affordable than rebuilding a foundation.

Here's an idea.
Many reputable foundation repair companies offer free inspections and written estimates, and if they are have been in business for a while, they also have some experience inspecting foundations for real estate transaction purposes.

I suggest you call a few of them, have at least one perform a professional inspection and give you a written estimate. With that written estimate you can then decide what you want to do. Walk away, negotiate down or ask the owner to fix.

Consider that the house will have to be fixed at some point. I believe the current owner will have to do it if he wants to sell the house.

Banks usually frown upon issuing loans to buy properties that have serious structural issues -- even if you are willing to buy it "as is" with a substantial discount.

But since you really like the house, it is a good idea to get an expert opinion, know exactly how serious the problem is and how much it will cost to fix it, since it won't cost you nothing to find out.

Hope this helps.

"I could keep the offer high, and then dicker after the inspection, when both parties are more "bound."

Based on the questions you asked, I am not sure you are ready for this type of heavy duty re-negotiation that extremely experienced and knowledgeable real estate investors are capable of doing. You could be the one who would be "bound" by your own high offer.

Hi. I have dealt with this situation. First, the little cottage that I rented and wanted to buy had a long crack in the cinderblock retaining wall. (Landlord would not negotiate price, so I walked away.) I moved on to purchase an adorable little bungalow built in 1924. The highest technology of the time involved stacking blocks one atop the other with no rebar to bind the wall together. Over 80 years the soil pushed the wall inward. There should not have been water near the foundation, but that is beside the point. Anyway, the eight foot high cinder block foundation started to break apart on the north side (not a bearing wall) to the point that I could push my hand through to the dirt. My workmen and I devised a way to dismantle the wall, build forms heavily reinforced with rebar, and they repoured the concrete wall, working from the inside. (I really don't believe in partial fixes. I wanted a structurally sound wall. That is what I got.)

You, however, are not working on the cheap as I was because this is not your problem to fix. The wall can be excavated and repaired from the outside. The sellers should have done this before listing the home. Why? Because a structural inspection will be necessary for any buyer to obtain a mortgage, and any structural engineer worth his or her salt is going to red flag that wall. You absolutely need to cease moving forward with the deal until you have 1) obtained a structural report and 2) gotten two or three estimates of repairs per that report. 3) Give this paperwork to the sellers and tell them to hop to it.

Don't freak out. You can do this. If the sellers are difficult, walk away--no, run. A classy seller would have resolved this issue up front. Good luck!