The small bodies community extends from near-sun to comets and KBOs. Somebody else will have to address the latter (or even main belt asteroids). You might look at early NEO community papers, e.g., from the big Asteroids volumes, for geometry-based NEO discovery arguments. Usually the survey volume was modeled more like an onion with enhanced detectability from the opposition phase effect. “Spherical” would also tend to imply that such a survey telescope operates at the center of the survey volume, which will never be the case for a ground-based facility due to limitations in operating near-sun.
The mega-constellations may limit LSST operations at low solar elongations, challenging the proposed twilight near-sun survey. Even small telescopes should continue to have access to a significant survey volume near-sun, e.g., comet hunters, large IEOs and small mini-moons. NEO Surveyor is anticipated to dominate at low solar elongations, including efficiently looking for Earth Trojans, but that is not the same thing as reaching a 100% success rate.
Numerous factors govern success with moving object discovery and both the Vera Rubin Observatory and NEO Surveyor project teams have addressed these issues through detailed object-by-object simulations. Both teams (with overlapping participation) have found a continuing need to include the contributions of the northern surveys to reach the 90% level for 140-m NEOs in an efficient manner. The LSST covers the south, NEO Surveyor alternately to the east and west, leaving significant areas of sky on any given night in the north for the ongoing surveys (or perhaps a new large-aperture NEO-optimized survey).
In your terms, the survey volume for the currently operating 1.5-1.8-m NEO projects reaches out past the orbit of Mars for 140-m objects. Apparent magnitude decreases steeply with distance, and the search radius will increase from that 1.5-1.6 AUs to about 2.0 AU (for 140-m objects of nominal albedo). The IR is different, but the numbers work out roughly similar for the 0.5-m NEO Surveyor which will have significant detectability to 140-m objects of all albedos out to again around 2.0 AU heliocentric distance. Less than that for smaller objects.
As you imply there is a different shell (the area swept out by the frustum of a cone might be better to model than a sphere) surveyed by the Rubin Observatory, NEO Surveyor, Catalina Sky Survey, and Pan-STARRS, as well as the smaller aperture telescopes like ZTF and ATLAS. Both the angular extent as well as the distance will vary between given contemporaneous observing sessions, and the ongoing NEO survey telescopes compare quite well with the Rubin field-of view. NEOs will enter the various survey volumes from many directions and at different rates (a result derivable from Granvik, et.al.) The sensitivity to small close-approachers and impactors will differ from 140-m objects, and for that matter there aren’t significant numbers of NEOs larger than 1-km remaining to be discovered by Rubin and NEO Surveyor.
The survey strategies are quite different as well as the cadence. LSST will require multiple visits over a week or two or more to link its candidate tracklets into detections. And NEO Surveyor will require a roughly similar interval before returning to a survey field on the same side of the sun to link significant discovery arcs. In the meantime, NEOCP-based rapid follow-up will continue to deliver near-real-time confirmation of targets accessible to the northern surveys. LSST and NEO Surveyor cadences will also adversely affect their sensitivity to rapidly moving objects. How all these factors interact is a complex convolution. To answer your final question, the various LSST / NEOCam simulations say the ongoing northern surveys will discover objects throughout, including 140-m objects. Discovery is a community activity and the surveys and follow-up facilities will benefit from coordinating operational strategies.