It seems clear that you already KNOW you want new knives.
Unfortunately, there are very few really good knife stores in the US. My understanding is that most "better knives" sold by brick and mortar stores are sold through kitchen or department stores. There are very few people working in kitchen stores who have much knife knowledge; and even fewer department store employees.
Equally as unfortunate, unless you have fairly well developed skills and going to a really good knife store and playing around with whatever a knife store (or knife department) has in stock is -- with certain exceptions -- far more likely to be misleading than helpful. Qualities like "heft," "balance" and eye-appeal are exaggerated there, while other qualities like long term comfort, profile, agility, lightness, edge taking and edge holding are given short shrift.
The Hattori HD are good for san-mai VG10. The Ryusens -- also san-mai VG10 -- are good but not quite as good the Hattoris. For what it's worth, Hattori and Ryusen have a working relationship in which Ryusen provides mass production capacity for Hattori, and the HDs are made in their joint factory, but finished by Hattori. I think, but am not sure, that the Ryusen Tsuchime are made in the same factory. I don't know the Shikis from experience, either my own or that of anyone's whom I trust.
Generally pattern welded san-mai VG10 knives tend not to be as good performers within a given price range (including your price range) as single steel knives made from other alloys. That's true for the Hattoris, true for the Ryusens, and probably true for the Shikis as well. For instance, you can get all the practical benefits of that type of knife for less than a hundred bucks with a Tojiro DP. But that doesn't mean that giving up a little bang-for-the-buck practicality and paying more for an aesthetic you really like is a bad decision. It depends on your priorities. Your priorities. Yours.
I don't want to get into a position where I'm describing the differences between a dozen or so knives with a couple of sentences for each one. That won't do much for you at your current state of "I don't know what I want." What would be helpful would be if you could decide:
- Whether you want a knife which can be easily maintained (but not sharpened) with a steel, or are willing to go to the stones to true;
- Whether you want a Japanese or Western style handle;
- Whether you want a knife which is very stiff or can accept some flexibility; and
- How often you're willing to switch away from your high performance gyuto to a something sturdier when faced with a "heavy-duty" task.
Perhaps more at issue is:
- How much time, trouble and money you're willing to invest in sharpening;
- Whether you're willing to learn basic knife skills.
An adequate board is less important, but still important.
Bottom line: Knives are tools. If money is at all in issue, don't waste it on tools which won't work for you.
Stay away from DMT and Lansky stones.
After everything is said and done an EP Apex is neither less convenient nor more convenient than bench stones. The advantages of an EP compared to bench stones is that it's easy to learn and will give you good results without too much practice. Its disadvantage are that it's not quite as versatile in terms of unusual knives, won't do big-deal profiling or repair as quickly, and that it's not cheap. If all you want to do is sharpen ordinary knives, and you can afford one, the EP is probably the better choice.