A wonderful (and useful) conversion guide.
Please consider my comments and suggestions.
\&\ as a and u in abut [ə], [ʌ] (unstressed/stressed respectively)
Both the stressed and the unstressed vowel in 'abut' can belong to one and the same phoneme only for those American speakers who do not have a phonetic distinction between them.
For those who have different phonetic values for the two vowels, the distinction is, as elsewhere, not only phonetic but phonemic, since /ʌ/ may occur in unstressed positions as well:
'unending' /ʌnˈɛndɪŋ/ vs 'an ending' /ənˈɛndɪŋ/.
WWWebster's transcription is representative of a widespread American accent where /ʌ/ and /ə/ have merged under a phonetic value more close to schwa [ə]. So I believe WWWebster's "&" is more likely to correspond to IPA [ə] only.
\&r\ as ur and er in further [ɝː], [ɚ] (stressed/unstressed r-coloured vowels; worry = [ˈwɝːiː])
(i) As above, for those Americans who do not make any distinction between the two, what is customarily transcribed as (ː)/ can occur in both stressed ('curve' /$ kɝv, £ kɜːv/) and unstressed ('excerpt' /$ˈɛksɝpt, £ˈɛksɜːpt/) positions. Again, I think IPA [ɚ] would be an adequate match for W's "&r".

(ii) I don't consider vowel length relevant to (phonemic) transcription of GenAm. In the standard accents of MnE quantitative phonemic opposition of vowels no longer exists -- all contrasts being qualitative. In transcribing RP, however, vowel length is, more often then not, marked. There are two reasons (or rather "excuses") for this: (a) in this way the "traditional" division of short vs long is preserved; (b) although not distinctive, the length of the "long vowels" is phonetically salient in RP.
In GenAm vowel length is by no means as prominent as in RP -- it is thoroughly conditioned by environment:
$/ɑ/ (/α/) : 'pa' [pʰɑː] ~ 'pod' [pʰɑˑd̥] ~ 'pot' [pʰɑt]; 'see' ~ 'seed' ~ 'seat'; etc. (Although in RP the same environmental conditions are operative, there are quantitative differences inherent to different phonemes -- /ɔː/ is inherently longer than /ɒ/.)
Furthermore, weak vowels are usually of rather short duration so I can't account for the length mark in the second syllable of your [ˈwɝːiː].

In the lines above I have been mostly concerned with the relevance of quantity to phonemic transcription of GenAm, and although your transcription is not explicitly phonemic, I find it unnecessary to state length in GenAm unless a very narrow transcription is intended.

\A\ as a in ace [eɪ] (a diphthong!)
Like GOAT, for many Americans it is a pure vowel -- [e(ː)].
\ä\ as o in mop [ɑ(ː)] (lengthened when stem-final, as in pa [ˈpɑː], in this position it may be replaced by [ɒː]) (underlining is mine)
$[ɑ(ː)] and [ɒ(ː)] (or up to [ɔ(ː)]) are in free variation in various other environments too: 'strong', 'dog', 'broad', 'brought', etc.
\E\ as ea in easy [iː] (usually slightly diphthongal [ɪi]; may be unstressed, as finally in very [ˈvɛɹiː])
WWWebster's "E" can stand both for a weak (and therefore inherently phonetically short) and a strong vowel — /i/; a length mark, if needed, should be added only to the strong vowel.
\hw\ as wh in what [ʍ] (= the voiceless counterpart of [w], also transcribed [hw]; most speakers use [w] instead)
Phonetically, [hw] is not the same as [ʍ], although together with [w] these are in free variation whenever the graphic realisation is < wh >. [hw] is a sequence of two sounds: "voiceless glottal fricative" + "voiced labio-velar approximant", while [ʍ] is a single sound — "voiceless labio-velar fricative".
All this variety is a reflection of the gradual lenition that took place since Old English: OE cluster < hw > [xw] developed into a single (voiceless) fricative — LOE, EME < hw, wh > [ʍ] (which is preserved in some accents), and then into an approximant — MnE < wh > [w]. The cluster that exists nowadays, [hw], is most probably an artificial formation, an attempt to imitate [ʍ] in order to keep < w > and < wh > apart. Indeed, many people (with no special ear training) will find [ʍ] and [hw] identical.
\l\ as l in lot [l] (pronounced as ‘dark’ [ɫ], except when followed by [j]; syllabic in bottle, whistle) (underlining is mine)
For many Americans /l/ is "dark" in all positions. I will never forget my first American teacher pronouncing 'volume' [ˈvɑɫjum] with a 100% valorized /l/.
\O\ as o in go [oʊ] (a diphthong; often unstressed, as in follow)
(i) As with [e(ː) ~ eɪ], this is often a pure vowel — [o(ː)].

(ii) Indeed, unstressed /o(ʊ)/ is (in J. Wells's theory of weak vowels) a weak vowel in GenAm. This is why it is much more frequent than RP (strong) /əʊ/: 'obituary' is usually /oʊˈbɪʧuɛri/ in GenAm, while the normal RP form, as regards the initial vowel, is /əˈbɪʧuəri/ (/əʊˈbɪʧuəri/ being typical of more careful speech).

Finally, I was wondering why you chose to use this kind of "inverted" slants, \\, for the normal ones — //.