Evidence for the interaction of SVLR and LLL
If two interacting processes are indeed operating in Scots/SSE, but only one in non-Scots dialects of English, one would expect a number of predictions to be borne out by instrumental measurements such as those from Agutter's study.

(1) The same degree of lengthening should be apparent in RP and Scots/SSE for all vowels in environments which are long for LLL but short for SVLR, that is before voiced stops, nasals and /l/.

(2) A rather greater increase in length should be found for all RP vowels before voiced fricatives and /r/ (and pre-pausally), in accordance with the general scale of lengthening contexts in (4.28), and the degree of lengthening in these environments should be comparable for those Scots vowels which are exceptions to SVLR.

(3) For those Scots/SSE vowels which are subject to SVLR, in SVLR long contexts, an extra increase in duration due to the operation of both SVLR and LLL would be expected.

In fact, Agutter's data can be shown to be consistent with these predictions, and thus with the hypothesis that two distinct rules are operating in Scots/SSE. In my reanalysis of these data, I have used only simple numerical analyses, which are robust and give a general indication of trends in the results; since Agutter's data lack balance and contain a number of gaps, I do not believe they merit complex statistical treatment.

In my reanalysis, I grouped Agutter's contexts into three rather than her two groups, labelled short, long and SVLR environments in (1).
(1) 

The vowels /ai/ and /i/ were grouped together, as both are generally agreed to be subject to SVLR, and /ɔ/ and /ɪ/ were combined, since both are generally classed as exceptions to SVLR. /au/ was kept separate, to ascertain which pattern it might be following. Grouping vowels is advantageous in partially compensating for the small sample size by spreading and de-emphasizing the effects of individual variation.

The values in (2) represent the mean durations in centiseconds for the three groups of vowels in each set of contexts and for each accent group, calculated from Agutter's measurements per vowel per speaker per context (Agutter 1988a: table 2). Where gaps occurred in Agutter's data due to mispronunciations or non-existence of lexical items, I excluded the context(s) with incomplete data for the subset of vowels concerned and for both accent groups. Standard errors were also calculated for each mean value, and are bracketed in (2).
(2) 

The values in (2) are graphed in (3), with error bars delimiting 95 per cent confidence intervals: these indicate that there is a probability of 95 per cent that the true population mean lies within this range.

In (3), RP vowels are universally longer than those of SSE speakers, except for the SVLR vowels /ai i/ in SVLR contexts, where this relationship is reversed. This trend is confirmed by a second set of calculations, again based on Agutter's data. Although, for reasons given above, I did not weight these results, the figures in (4) do represent a certain amount of standardization. Here, the mean duration of each vowel group in short contexts is taken as the base, or 100 per cent, since no environmentally conditioned lengthening is assumed to be operating here. Vowel duration in long and SVLR environments is then expressed as a proportion of length in the short contexts. This assumption of a common base enables a comparison of like with like.

Although (2) and (3) make it clear that /au/ is behaving like /ɔ ɪ/ rather than /ai i/ in SSE, I have not combined the values for /au/ with those for /ɔ ɪ/, since these three vowels all exhibit gaps in the data in different contexts, and my policy on such gaps would involve unacceptably reducing the number of data points for a combined class.
(3) 
(4) 

It is clear from the percentage figures in (4), and the histogram derived from these in (5), that all vowels in RP and all SSE vowels apart from /ai i/ in SVLR environments follow an equivalent pattern of lengthening, with 30-40% extra duration in long environments and a further 10-25% in the universally longer SVLR environments (the extreme contexts from the LLL schema). However, for only those vowels which are traditionally classed as subject to SVLR, and in SVLR long environments, a far greater degree of lengthening can be observed in SSE. /ai i/ lengthen by around 40% over short contexts in long environments in RP and SSE. If one process is responsible for all durational variation shown in (4), SSE /ai i/ should then show approximately 50-65% extra duration in SVLR contexts over short ones. However, the actual increase for /ai i/ is 96.6%, 27.7% greater than the percentage increase for the equivalent set of RP vowels.

My assertion that this extra duration is due to SVLR might be challenged in view of the fact that /ɔ ɪ/, the supposed exceptions to SVLR, lengthen by 59.6% in SVLR over short contexts in SSE, but by only 34.8% in RP, with a similar extra increase for SSE of 24.8%. However, as the histogram in (5) makes clear, this discrepancy is due to the failure of RP /ɔ ɪ/ to lengthen by the expected amount in long contexts, while SSE /ɔ ɪ/ do follow the general pattern here. In both cases the difference between long and SVLR contexts is approximately 20%. Thus, the apparent extra lengthening for SSE /ɔ ɪ/ is actually due to differences in the behavior of the relevant vowels in long rather than in SVLR environments, and is probably an artefact of the experiment caused by the small number of informants in the RP class.

Around 25-30% of the durational change for /ai i/ alone, in SSE and in SVLR long environments, cannot be accounted for given Agutter's contention that one rule can explain all the attested length variation in both RP and SSE. On the other hand, these results are of exactly the type predicted if two processes, operating in partially overlapping environments, are involved; LLL, common to both accents, produces the shared lengthening seen in (2)-(5), while SVLR accounts for the peculiarly Scottish additional lengthening which affects /ai i/ (and a variable set of other vowels not tested by Agutter) in the traditional SVLR environments.

(5)