Okay, let's break down your questions about storable pools and related electrical requirements.

Definition of "Storable" in 680

The NEC doesn't explicitly define "storable" in a single sentence. However, the context within Article 680, Part II (Permanently Installed Pools) and Part III (Storable Pools) makes the distinction clear. Think of it this way: Storable

Pools that are constructed so that they may be readily disassembled for storage and reassembled to their original dimensions. Think of inflatable pools, pools with metal or plastic frames that can be taken apart, and similar portable structures. The key is the easy disassembly and storage aspect.

Permanently Installed

Pools constructed in the ground or on the ground that cannot be readily disassembled for storage.

Your Patio Unit

Based on your description ("prepackaged unit that you lay on a patio"), it sounds like a storable pool, if it can be easily disassembled and stored. If it requires any significant construction/demolition to remove, then it's likely permanently installed. It comes down to ease of disassembly.

"Self-Contained"

The term "self-contained" doesn't appear as a defined term in NEC Article 680. In the context of pools, it generally refers to equipment that integrates multiple functions into a single unit. This is more common with permanently installed pools for example: a self-contained pool filter and pump. Self-contained hot tubs and spas are addressed under 680.
40.

Emergency Shutoff Switch (680.41)

The NEC 680.41 only states that the emergency shutoff switch must be "readily accessible" and "clearly labeled." It doesn't specify a lever-style or toggle switch. A pull-out style disconnect, similar to those used for AC units, could be code-compliant as long as it meets these conditions:1. Readily Accessible

Easily reachable in an emergency.2.

Clearly Labeled

Must be clearly marked as an emergency shutoff for the pool equipment.3.

Interrupts ALL ungrounded conductors

The disconnect has to cut the power to all the hot wires feeding the equipment.4.

Within Sight

Must be located at least 5' from and within sight of the pool or spa.

Trenching Who to Hire

Landscapers are a good choice for trenching, especially if you need to restore the area afterward. You can also look for general contractors, excavators, or even some electricians may offer trenching services.

DIY Trenching

Trenching 60 feet can be a significant amount of work, even with power tools. The difficulty depends on:

Soil Type

Rocky or dense clay soil is much harder than loose dirt.

Depth and Width

Deeper and wider trenches require more digging. Check local code for burial depth requirements.

Root Systems

Tree and shrub roots can be a major obstacle.

Equipment

A trenching machine (rentable) will make the job much faster and easier than a shovel. Even a heavy-duty pickaxe can help break up hard soil.

Underground Utilities

This is the BIGGEST concern.

ALWAYS call 811 (Call Before You Dig) to have underground utilities located before you start digging. Striking a gas or electrical line can be deadly.

It's a PITA Rating (Power Tool Assisted)

Easy Soil, No Obstacles: 3/10 (Tedious, but manageable) Moderate Soil, Some Roots: 6/10 (Requires some effort and patience) Rocky/Clay Soil, Lots of Roots: 9/10 (Consider hiring it out)

Wire Size (#6 vs. #8)

You are likely required to follow the manufacturer's installation instructions and use #6 wire if that's what they specify. Here's why: UL Listing (or similar)

The pool equipment is likely UL listed (or a similar safety certification). That listing is based on the product being installed according to the manufacturer's instructions. Deviating from those instructions can void the listing and potentially create a safety hazard.

Liability

If something goes wrong and the equipment fails (or worse, causes a fire or injury) and you didn't follow the instructions, you could be held liable.

Other Considerations

The manufacturer might have specified #6 wire for reasons beyond voltage drop. It could be related to heat dissipation, long-term reliability, or internal wiring within the unit that is sized for #6.

In summary, while your calculations may show that #8 wire appears* sufficient for voltage drop, you should follow the manufacturer's instructions and use #6 wire. Flag for review