You might try listening to recordings by sopranos Arleen Auger, & Elly Ameling, and mezzo-soprano Dame Janet Baker in Schubert lieder. One of Schubert's best known songs that you didn't mention is "Der Hirt auf dem Felsen" or "The Shepherd on the Rock"--for soprano, piano, & clarinet. It's a favorite of mine, although it may not be exactly what you're looking for (I'm not sure). It may also partly depend on who's singing it. Sopranos Ameling & Auger have done excellent (but contrasting) versions. Here's a link to Ameling's recording (while Auger's is on her album with Graham Johnson that I've linked below):
1. However, I'd suggest that you start with Schubert's Goethe lieder (which includes Gretchen am Spinnrade, D. 118), sung by Auger, with pianist Walter Olbertz, as a selection of these songs closely fit what you're asking for (though maybe not all):
https://www.amazon.com/Schubert-Goe...0035QQ/ref=sr_1_8?s=music&ie=UTF8&qid=1539463219&sr=1-8&keywords=auger+schubert
The following Auger album from pianist Graham Johnson's extensive Schubert lieder survey for Hyperion is another favorite of mine:
https://www.amazon.com/Hyperion-Sch...002ZF3/ref=sr_1_1?s=music&ie=UTF8&qid=1539463219&sr=1-1&keywords=auger+schubert
Auger also did a Schubert lieder album with pianist Lambert Orkis (on a historical piano--which is worth hearing):
https://www.amazon.com/Schubert-Lie...mr0_2?s=music&ie=UTF8&qid=1539466054&sr=8-2-fkmr0&keywords=auger+schubert+works
or
https://www.amazon.com/Schubert-Arl.../dp/B003WJ6QB8/ref=sr_1_6?ie=UTF8&qid=1539466112&sr=8-6&keywords=auger+schubert
2. Dame Janet Baker: especially her 'classic' Schubert recordings with pianist Gerald Moore:
https://www.amazon.com/Schubert-Lie.../ref=sr_1_4?s=music&ie=UTF8&qid=1539463328&sr=1-4&keywords=Baker+janet+schubert
https://www.amazon.com/Schubert-Lie...sr_1_5?ie=UTF8&qid=1539466902&sr=8-5&keywords=janet+baker+gerald+moore+schubert
The old Seraphim LPs (personal nostalgia on my part):
https://www.amazon.com/Janet-Baker-...B002BRNG4M/ref=sr_1_1?ie=UTF8&qid=1539466859&sr=8-1&keywords=janet+baker+double
3. Elly Ameling:
Here are links to four 'desert island' Ameling/Schubert discs of mine (note that the Pentatone hybrid SACDs catch Ameling's beautiful voice especially well, although the Philips CD is probably the more essential):
https://www.amazon.com/Elly-Ameling...AC5T61T&pf_rd_s=desktop-dp-sims&pf_rd_t=40701&psc=1&refRID=XHJ30RGVAK68BAC5T61T--recorded early in Ameling's career, & her voice is especially pure & beautiful. The disc also includes Ameling's version of "The Shepherd on the Rock" mentioned above. Here too is an alternative reissue of the same recording:
https://www.amazon.com/Elly-Ameling...1TVW/ref=sr_1_6?s=music&ie=UTF8&qid=1539468330&sr=1-6&keywords=ameling+schubert
https://www.amazon.com/Schubert-Ave...40ZA/ref=sr_1_4?s=music&ie=UTF8&qid=1539463364&sr=1-4&keywords=Ameling+schubert--a classic Schubert recording.
https://www.amazon.com/Frauenliebe-...ref=sr_1_2?s=music&ie=UTF8&qid=1539463489&sr=1-2&keywords=Ameling+schubert+sacd
https://www.amazon.com/Lieder-Franz...ref=sr_1_3?s=music&ie=UTF8&qid=1539463489&sr=1-3&keywords=Ameling+schubert+sacd
Two of Ameling's Schubert recordings that was made later in her career:
https://www.amazon.com/Ameling-Sing...G9C2/ref=sr_1_1?s=music&ie=UTF8&qid=1539463364&sr=1-1&keywords=Ameling+schubert
https://www.amazon.com/Die-Musik-Fr...LQ/ref=sr_1_10?s=music&ie=UTF8&qid=1539463364&sr=1-10&keywords=Ameling+schubert
4. Gundula Janowitz is also excellent in Schubert lieder, and another soprano whose recordings you may wish to sample at some point:
https://www.amazon.com/Lieder-Gundu...sr_1_1?s=music&ie=UTF8&qid=1539463980&sr=1-1&keywords=gundula+janowitz+schubert
https://www.amazon.com/Schubert-Lie...sr_1_2?s=music&ie=UTF8&qid=1539463980&sr=1-2&keywords=gundula+janowitz+schubert
5. Elisabeth Schwarzkopf's Schubert lieder recordings with pianist Edwin Fischer are highly regarded too (although they were recorded in mono sound, and I personally prefer Ameling, Auger, Baker, & Janowitz in Schubert myself; even though Edwin Fischer is a favorite pianist of mine. I mention this recording because it's a favorite of others, and it won a 'rosette' award from the old Penquin Guide.):
https://www.amazon.com/Schubert-Lie...1_6?s=music&ie=UTF8&qid=1539463640&sr=1-6&keywords=fischer+schwarzkopf+schubert
6. Here's another excellent Schubert recital to explore, given by American soprano Cheryl Studer, with pianist Irwin Gage:
Considering that it's so easy to sample recordings these days for free, if you take the time to explore the above recordings, I expect you'll make many new discoveries along the lines of what you're looking for (& hear the songs in very fine performances).
I'd also strongly urge you to eventually explore the lieder of Robert Schumann as well, down the road, since Schumann was arguably an even finer lieder composer than Schubert (in my view); along with the songs of Hugo Wolf and Johannes Brahms.
Hope that helps.