You're on the right track, actually.
There aren't many generator designs out there, at least that I've seen, other than commercial test equipment of course; but I have seen two online. I will present them here.
JASO D 001-94 Type A-1
This standard specifies the RC network, generator circuit, and provides suitable values to use in it. It looks like copies may be available online. From p.8-9:
Interestingly, they also suggest using an alternator as such (Fig. 5)!
Here are the values. Type A is for 12V systems, B for 24V. Type 1 is the "load dump" surge in question.
Backfeeding is easily avoided: usually a diode-wired-OR connection allows the surge generator to drive the load during, while the main (12V) supply provides steady power otherwise. This diagram shows a diode from E1 only, but a diode from the generator side to the EUT (Equipment Under Test) could easily be added, making suitable adjustments for voltage drop.
Note that the risetime of the switch closure will be extremely short; this violates the specifications of ISO 7637-2 or ISO 16750-2, for which an RC filtering circuit (of low ~ms time constant) would have to be added, and the amplitude adjusted to account for peak loss through the filter.
On the other hand, perhaps you just want a representative idea of how well your device performs, and the fast risetime provides an opportunity to observe how tolerant it is of faster transients, or hard switching. Definitely some possibility to discover ringing or overshoot of ceramic capacitors this way.
An active generator design is available from the good fellows at Analog Devices (née Linear Technology):
DEMO MANUAL DC1950A: Load Dump Generator | Linear Technology
This circuit uses a fixed power supply (could also be a capacitor charged up by a much weaker supply), and a couple, rather beefy, MOSFETs to deliver the pulse. Given the power dissipation ratings, and specialized type (IXYS/Littelfuse Linear L2: suitable for linear amplification use, wide SOA), you'd have to spend a few bucks building one -- but it's a pretty straightforward circuit, and looks competently designed.
I would say IXTX90N25L2 and IXTX110N20L2 are both acceptable here. You might make do with classic HEXFETs such as IRFP260 or bigger, but you'll have to evaluate the SOA yourself -- a problem exacerbated by the fact that no datasheets beyond the 1980s originals specify DC SOA, and most likely you'll need to use many more in parallel. The circuit is easily scaled to more parallel devices, at least.
Do not use modern MOSFETs, or BJTs, by the way. Or, not just anything. As a linear application, DC (or at least ~100ms) SOA is required here, and most parts exhibit 2nd breakdown (localized spot heating leading to instability and runaway failure). Check the datasheet, and see how much power can be dissipated, continuously (or at least for 10s ms), at significant voltage; if there's no such rating, skip it and go to the next.
The main reason to avoid modern MOSFETs though, is they're just so much smaller for the same V, I ratings. Power dissipation capacity maps to die size, and they've done a tremendous job shrinking die area (maximizing power-switching density).
Even if you had wide-SOA BJTs (there are some still available for audio power amplifier use, that would work here, actually), they would need further circuit changes anyway. But not a whole lot; say, an IRF640 source follower into BJT bases, would solve that pretty neatly. In other words, making a sort of hybrid Darlington device, in place of the MOSFET(s) as shown. Or in still other words: to basically construct a variant IGBT. Oh, on that note: don't use IGBTs either -- same problem, no SOA. Although, I have actually seen a couple IGBTs with DC SOA, which, I don't have a clue how or why they do (why did they bother testing it? How does the design not runaway instantly?), but, there are indeed a few out there, so... that's interesting?
If you know, as a matter of design principle, or by measuring it directly, that your device does not draw significant current during the surge, then the generator impedance can be much higher, while still developing the specified voltage waveform. This greatly reduces the size of transistors and capacitors (or power supplies) required.
This is, in effect, the basis of Dave Tweed's answer; though the inductive method suggested, has the drawback of having to locate an inductor of rather unusual rating. Still, it can produce such a waveform, given you don't need to draw much current in the process.
I would guess all commercial units use capacitive energy storage, and if any use magnetics, it's going to be with a real spinning alternator.
 A 1H 1A+ inductor will be quite large, and it can't saturate, you can't simply use a power transformer for it (there must be an air gap in the core to store energy). Though, one might profitably look into microwave oven transformers, where the core can be split open (with a hacksaw or grinder), and an air gap introduced; the high-voltage secondary can be removed, and even replaced with another primary, if one has a matched pair of transformers to scrounge from. (The secondary has far too much resistance to be useful here, unfortunately.) I still don't think the inductance will be quite high enough, but maybe with a pair of 240V primaries wired in series, it'll get close..?