I would purchase a higher quality freestanding and place quality and knobs out of reach over aesthetic.

I would choose induction over non-induction regardless of aesthetics or location of knobs. Even if the tot could turn on the induction cooktop, they won't get badly burned with induction - in fact, without a pot or pan on the cooktop, nothing will even get hot. So it's not important to lock the controls, what's important is to keep pots and pans put away.

Get the induction range for the reasons that sjhockey and sreedesq gave plus these.

The top cooking surface on most electric slide-ins (both radiant and induction) will be more confined than on free-standing ranges. You would not think so but most of them have slanted control panels at the front which eat more space than you might guess. This might or might not be a concern for you.

You are replacing a freestanding range that sits flush against the back wall. Many electric slide-in ranges have an oven "bump-out" at the back. That means the stove top will not butt flush to the back wall. Having one of those will require a countertop fiiller strip or cover of some kind back there to fill the space from the back edge of the stovetop to the wall. (A recent post here on slide-ins also pointed out that those slide-in ranges that do go flush to a back wall and those which sit in an island also may have 1" gaps at the back corners, too.) Something to consider since your countertops are already in place.

For the built-in look you like, your countertops can't have raised "drip-stop" bulges at the front edge (from your photo, seems not a problem for your kitchen) and there can be a gap between the countertop and the slide-ins' stovetop overhangs if your countertops are not close to 36" high. (Many standard base cabinets and countertops only go up to 35¼" to 35½" high.) This might or might not be a problem with your counters.

You also would need to put something non-flammable on the wall behind the slide-in range, from 5 or 6 inches below the cooktop on up to the OTR. You could tile a backsplash. Many hardware stores sell stainless and painted sheet metal plates for this and metal shops can easily fabricate one for you. Another option is mounting a tempered glass plate (frosted side to the wall, smooth side out) which you can order through a local glass shop.

Also, it looks like your OTR (over the range) will be a recirculating unit rather an being set-up to vent externally. Induction will produce significantly less waste heat than a radiant electric stove-top, so the kitchen may be less uncomfortable when cooking in the summer.

If you really have your heart set on a slide-in, there is one induction slide-in that may be within your budget, the newish Frigidaire FGIS3065PF. With July 4th sales "events" going on, the price seems to be in the $1500 to $1700 range, depending on where you shop.

The "yes, but" items for this slide-in range are: (a) as with the radiant electric versions of this range, the oven vent is at the front of the range, right beneath the oven control panel (a design which has led to some complaints on the radiant-topped versions of this range); (b) the oven cavity is not as large as on most freestanding induction ranges (which may or may not be a consideration for you); and (c) it is is one of the slide-in ranges that will not go flush to the back wall.