You can choose your own box from a museum or archival supplier, like Hollinger Metal Edge (they have window display boxes, but only 3″ deep – it would depend on how fluffy your dress is) and DIY it after you get it cleaned. Just be very careful when looking at the materials. I’ve never dealt with the company you mention, but I can’t find the specs for their boxes on their site, which makes me nervous.
When I do textile preservation, I don’t use window boxes. They don’t offer the same protection as other archival boxes, and textiles require special care to remain stable over time. Still, it’s up to you! Here are a few resources to consider:
This pamphlet from Museum Textiles lists a lot of pros and cons to consider when looking at the various methods of gown preservation and what to look for when you’ve picked one. The biggies: you want to store flat if you can’t store hanging. Avoid colored tissues or colored boxes. Be wary of window boxes, and if you opt for window boxes, make sure they pass the PAT test and have no plastic, just polyester or other safe poly materials that won’t hasten the breakdown of your fabric.
This article from Archival Methods takes you through the steps of storing textiles for long term preservation, and unlike the other, it has pictures. 🙂 It assumes you’re not using a window box, but they also get into the details of the process that will be useful no matter what box you would choose. One note – I don’t think you need to worry about the dessicant. If the dress if properly cleaned before you store it and you have a clean setup and the proper materials as they direct, you won’t need it. I’ve never had to use a dessicant when I store historic textiles.
Other things to consider – check around for local and state historical societies to see if they have any workshops on textile preservation. Or any museum studies or archives programs where you might be able to enlist a starving grad student or new professional to do it for you with all the skill but half the cost so they can boost their resume.
And ask yourself very honestly how often and how long you intend to display the dress. There are a lot of gown preservation kits from Hollinger, Gaylord Archival, and just about every other archives/museum supplier, but they virtually never have window boxes. Would you consider getting a window box for the short term and then putting it into dark preservation for the long term? You would still be able to take it out and display when the mood suited you. No textile should be on constant display and constant exposure to light – even though wedding gowns tend to be white, not only dyes but the fabric fibers themselves break down when exposed too long, and once that process starts, it can’t be stopped no matter how much action is taken. (This is why textile museums are so dark.)
There, that is the way-too-long answer to your question. 🙂 I am biased. This is part of what I do for a living.