I have not found one with a convincing organ sound at any price. You're trying to get one keyboard that will do two or three things well. You want a portable piano that can also emulate a quality organ that also has good speakers.
For a hammer-action weighted keyboard, generally that's true except for some stage keyboards outside the OP's price range, like the Nord Stage models.
However a Nord Electro can be had in 61 or 73 keys, the keys are designed to resemble an organ's, and has decent acoustic/electric pianos (acceptable, I'd say, probably, at best, compared to the far superior SK-1), and I believe a harpsichord of some kind (the company has a bunch of options for downloading newer samples directly to the keyboard, so that's very likely been taken care of). Should be had on the cheap, used.
But, it is bright red in color, and, of course, doesn't have any speakers.
There is
ONE practical problem with using the MIDI software solution. That's the kind of "controller" (i.e., keyboard) one uses.
It's true, even a child's instrument will do the job fine. Press a key, you'll get the sound you want from your software synthesizer/sampler.
But without a more specialized controller, one's likely going to be limited to at most a few buttons you can assign to change pre-sets. And not much flexibility if you want to split the keyboard to have, say, the top half "be" one manual and the bottom half "be" a different manual of an organ. And options for expression pedals, sustain pedals, all that. If there are any true controllers still made, without onboard sounds, they should be still fairly cheap compared to entry-level romplers, and if used is the way to go, they're generally very robust, practical gear designed for musicians on the road and in rugged, variable conditions.
And it still won't have speakers, just the audio interface from your computing device (or out of one of the one of the increasingly rare hardware rack-mount units, like the Yamaha Motif racks, which could actually fill the bill pretty well....I don't know if they're making them anymore, but it's a good, versatile set of samples, with passable organs, some harpsichords, acoustic pianos).
Yeah, so, it depends on what level of control you want at your fingertips on the keyboard itself, vs "swiping" on a tablet computer, for example, to change sounds/parameters.
If you go the SoftSynth route.
I don't think there's anything remotely in the OP's budget with a weighted action and on-board, flexible, top-quality sounds. Certainly not with speakers built in. You could pay somebody to put some little speakers and add a power amp stage to the balanced outs, or do it yourself. What's the problem with using your Genelecs? Are they broken or something?
But, there are several unweighted, organistic keyboards with plenty of control options on the keyboard itself that can be had pushing up to the budgetary limit, as suggested above. No, none of those have any built-in speakers.
Anyway, the short of it is that, unless moving up to a Nord Stage or something like a Yamaha Motif/MODX or a Korg Kronos workstation, one isn't going to have it all in one package. But there are strengths and weaknesses in those, too.
The built-in speakers is a pipe dream, so to speak, IMHO, for a professional instrument ready-to-go out of the box.
I would say those are facts, with the same proviso as
timothy42b: just what I know about it. I'm resigned to using two keyboards, always: organ on top, hammer-action acoustic/electric piano below.
Organ doesn't seem like an organ to me on weighted keys, and a piano on unweighted/semi-weighted keys is not right either. Sure, either sound
can be played on whatever action, but beyond rudimentary things, I can't make either instrument happen with the "wrong" action.
And, at home, like
timothy42b, I've stopped using a 15" JBL powered monitor and just go through a consumer-grade home-theater amplifier with I think five tiny speakers and a subwoofer, in between which there's a Mackie mixer to add some flexibility (SM57 to an XLR channel to yell at the neighbors, extra inputs for different keyboards or guitar, etc.), and it's fine.
3. an actual portable organ like a Hammond B3, but now it won't sit on a table.
Which *also* needs a speaker and amplifier, lest you forget!

No, the real sticking point is built-in speakers. Just not going to happen, at least with high-quality sounds among organs, pianos, and harpsichords.
But, then again, Casio has been in the past, say, twenty years, fooled everybody and produced extremely high-quality acoustic pianos at a lower price with things like built-in speakers: I have no idea the state of their core organ samples, nor harpsichords, but I wouldn't rule out some of the lower-end Casio or Yamahas.
It just depends on how "good" one wants the sounds, I guess, but price is not much any longer an absolute indicator of quality, even including items like built-in-speakers: sometimes "good enough" is indeed good enough. Just depends on which instruments one plays the most, I suppose.
Generally, stage equipment doesn't bother to include the extra weight of even small speakers and a power amplifier, since there's no need, but there are always compromises at the lower end.
/* Edited To Add: what's with the built-in speakers fetish? Not directly to the OP, but it seems more people, this is a deal-breaker. Yeah, I'm actually shopping for a little Yamaha AP with speakers, just for the convenience, but since when does any gear come with its own amplification and speakers? Aside from acoustic instruments.
It's nice, but c'mon, it's not an acoustic instrument! To me, that's like shopping around for a toy like a "backpacker's guitar" or something. I want one, but that's not a reasonable expectation of a good instrument, where the target audience uses the gear in concert with other instruments etc.
And, also, who the heck plays music standing their instrument on some table? There are things called keyboard stands that work very well.
I'm always shopping around for a little hammer-action keyboard with built-in speakers, and, ideally, DC power adapter, but, let's be real: I need a case for it that likely is the same as the cost of the instrument, and deal with inferior sounds.
For my uses, that's fine, but that's not what people would use on stage. A little Yamaha $300 digital piano, put with a $300 SKB case is worth it to me, but I know what I'm buying, and to me that's fine, but I'm using that for one specific purpose only.
That's a reason:
I don't know, but I'd rather accept the compromises and deal with it. No board does it all, a table is not a keyboard stand, and so forth. */